Three-dimensional printing of three-dimensional objects

ABSTRACT

The present disclosure provides three-dimensional (3D) printing methods, apparatuses, systems and/or software to form one or more three-dimensional objects, some of which may be complex. The three-dimensional objects may be formed by three-dimensional printing using one or more methodologies. In some embodiments, the three-dimensional object may comprise an overhang portion, such as a cavity ceiling, with diminished deformation and/or auxiliary support structures.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims benefit of prior-filed U.S. Provisional PatentApplication Ser. No. 62/466,280, filed Mar. 2, 2017, and U.S.Provisional Patent Application Ser. No. 62/539,990, filed Aug. 1, 2017,each of which is entirely incorporated herein by reference.

BACKGROUND

Three-dimensional (3D) printing (e.g., additive manufacturing) is aprocess for making a three-dimensional (3D) object of any shape from adesign. The design may be in the form of a data source such as anelectronic data source or may be in the form of a hard copy. The hardcopy may be a two-dimensional representation of a 3D object. The datasource may be an electronic 3D model. 3D minting may be accomplishedthrough an additive process in which successive layers of material arelaid down one on top of each other. This process may be controlled(e.g., computer controlled, manually controlled, or both). A 3D printercan be an industrial robot.

3D printing can generate custom parts quickly and efficiently. A varietyof materials can be used in a 3D printing process including elementalmetal, metal alloy, ceramic, elemental carbon, or polymeric material. Ina typical additive 3D printing process, a first material-layer isformed, and thereafter, successive material-layers (or parts thereof)are added one by one, wherein each new material-layer is added on apre-formed material-layer, until the entire designed three-dimensionalstructure (3D object) is materialized.

3D models may be created utilizing a computer aided design package orvia 3D scanner. The manual modeling process of preparing geometric datafor 3D computer graphics may be like plastic arts, such as sculpting oranimating. 3D scanning is a process of analyzing and collecting digitaldata on the shape and appearance of a real object. Based on this data,3D models of the scanned object can be produced. The 3D models mayinclude computer-aided design (CAD).

A large number of additive processes are currently available. They maydiffer in the manner layers are deposited to create the materializedstructure. They may vary in the material or materials that are used togenerate the designed structure. Some methods melt or soften material toproduce the layers. Examples for 3D printing methods include selectivelaser melting (SLM), selective laser sintering (SLS), direct metal lasersintering (DMLS), shape deposition manufacturing (SDM) or fuseddeposition modeling (FDM). Other methods cure liquid materials usingdifferent technologies such as stereo lithography (SLA). In the methodof laminated object manufacturing (LOM), thin layers (made inter alia ofpaper, polymer, metal) are cut to shape and joined together.

Sometimes, it is requested to control the microstructure of a 3D objectto form a specific type or types of microstructure (e.g., grain (e.g.,crystal) structure and/or metallurgical microstructure). At times, it isrequested to fabricate a 3D object including complex topology (e.g.,intricate, and/or fine microstructures). For example, the 3D object maycomprise overhangs (e.g., ledges), and/or cavities. Occasionally, it isrequested to fabricate a 3D object with varied materials and/or materialstructures in specific portions of the 3D object. The present disclosuredescribes formation of such requested 3D objects. In some instances, itis requested to control the way at least a portion of a layer ofhardened material is formed. The layer of hardened material may comprisea multiplicity of melt pools. In some instances, it may be requested tocontrol one or more characteristics of the melt pool that forms thelayer of hardened material.

At times, the printed 3D object may bend, warp, roll, cud, or otherwisedeform during the 3D printing process. Auxiliary supports may beinserted to circumvent the deformation. These auxiliary supports may besubsequently removed from the printed 3D object to produce a requested3D product (e.g., 3D object). The presence of auxiliary supports mayincrease the cost and time required to manufacture the 3D object. Attimes, the requirement for the presence of auxiliary supports hinders(e.g., prevent) formation of cavities and/or ledges in the requested 3Dobject. The requirement for the presence of auxiliary supports may placeconstraints on the design of 3D objects, and/or on their respectivematerialization. In some embodiments, the inventions in the presentdisclosure facilitate the generation of 3D objects with reduced degreeof deformation. In some embodiments, the inventions in the presentdisclosure facilitate generation of 3D objects that are fabricated withdiminished number (e.g., absence) of auxiliary supports (e.g., withoutauxiliary supports). In some embodiments, the inventions in the presentdisclosure facilitate generation of 3D objects with diminished amount ofdesign and/or fabrication constraints (referred to herein as“constraint-less 3D object”).

SUMMARY

In an aspect described herein are methods, systems, apparatuses, and/orsoftware for generating a 3D object comprising a metal alloy bydiffusion. The diffusion may comprise diffusion of at least a firstelement into a material deficient in that first element. The diffusionmay be controlled. The diffusion may result in a homogenous distributionof crystal phases and/or metallurgical morphologies. The diffusion mayresult in a 3D object comprising diminished number of defects. Thedefects may comprise fractures. The fractures may comprise heat cracks.

In another aspect, a method of printing a three-dimensional objectcomprises: (a) transforming a first pre-transformed material to a firsttransformed material to print a layer of hardened material as part ofthe three-dimensional object, which layer comprises a pore; and (b)using an energy beam to density the second transformed material toreduce or eliminate the pore. In some embodiments, using the energy beamcomprises re-transforming the transformed material. In some embodiments,transforming comprises melting. In some embodiments, melting is completemelting to a liquid state. In some embodiments, transforming inoperation (a) comprises generating a melt pool having one aspect ratio(e.g., globular melt pool). In some embodiments, transforming inoperation (b) comprises generating a inch pool of a different aspectratio than the one aspect ratio. A different aspect ratio may be ahigher aspect ratio than the one aspect ratio (e.g., generating a highaspect ratio melt pool). A different aspect ratio may be generating amelt pool that is narrower and/or deeper relative to the one aspectratio.

In another aspect, printing a three-dimensional object comprises: (a)using a first energy beam to transform one or more layers ofpre-transformed material to print one or more layers of transformedmaterial; and (b) using a second energy beam to reduce a porosity of theone or more layers of transformed material, wherein reducing theporosity comprises transforming at least a portion of each of the one ormore layers of transformed material.

In some embodiments, the first energy beam moves at a slower speed alongits path relative to the second energy beam (e.g., by an order ofmagnitude). In some embodiments, the first energy beam has a powerdensity that is lower than a power density of the second energy beam(e.g., by an order of magnitude). In some embodiments, the power densityprofile of the second energy beam during irradiation is different fromthe power density of the first energy beam during it irradiation. Insome embodiments, the power density profile of the first energy beamand/or second energy beam is controlled in real time during theirrespective irradiation. In some embodiments. (a) comprises forming afirst melt pool. In some embodiments, (b) comprises forming a secondmelt pool. In some embodiments, the second melt pool has a higher aspectratio than the first melt pool. In some embodiments, (b) comprisesforming a melt pool having a depth that is greater than a radius of anexposed surface of the melt pool. In some embodiments, the depth is atleast twice the radius of the exposed surface of the melt pool. In someembodiments, forming the melt pool comprises forming a well in a centralregion of the melt pool. In some embodiments, the method furthercomprises laterally elongating the well by laterally moving the secondenergy beam. In some embodiments.6, the method further comprises (e.g.,gradually) lowering an intensity of the second energy beam during dielateral movement to allow closure of the well. In some embodiments,using the second energy beam to reduce the porosity comprises alters amicrostructure of the or more layers of transformed material. In someembodiments, (b) increases a density of the or more layers oftransformed material by at least about 85%, 95.5%, or 110%. In someembodiments, (a) comprises forming at least two layers of transformedmaterial. In some embodiments, (b) comprises reducing a porosity of theat least two layers of transformed material. In some embodiments, (b)comprises reducing a volume percentage porosity and/or an areapercentage porosity of the at least two layers of transformed materialby at least about one order of magnitude. In some embodiments, (b)comprises reducing an area percentage porosity of the at least twolayers of transformed material by at least about one order of magnitude.In some embodiments, (b) comprises melting at least a portion of each ofthe at least two layers of transformed material. In some embodiments,the one or more layers of transformed material define a layering planeindicative (e.g., characteristic, or typical) of a layerwise printing ofthe three-dimensional object. In some embodiments, the one or morelayers of transformed material are part of an overhang of thethree-dimensional object. In some embodiments, a vector normal to asurface at a point on an exterior surface of the overhang forms an anglewith respect to (i) the layering plane that intersects the vector or to(ii) a plane parallel to the layering plane that intersects the vector.In some embodiments, at least one characteristic of the first energybeam is different from a respective one of the second energy beam. Insome embodiments, the at least one characteristic of the first energybeam comprises a power density, a scanning speed, a dwell time, anintermission time, or a cross-section. In some embodiments, the powerdensity of the second energy beam is greater than the power density ofthe first energy beam. In some embodiments, the power density of thesecond energy beam is smaller than the power density of the first energybeam. In some embodiments, a scan speed of the second energy beam is:faster than a scan speed of the first energy beam. In some embodiments,a scan speed of the second energy beam scanning speed is slower than ascan speed of the first energy beam. In some embodiments, the firstenergy beam is stationary or substantially stationary about a pointduring the dwell time. In some embodiments, transforming in (a) and/or(b) comprises forming a plurality of tiles by: (i) transforming apre-transformed material to a first transformed material at a firstposition on a target surface using the first energy beam during a firsttime period to form a first tile, which first position is along apath-of-tiles, wherein during the first time period, the first energybeam is stationary or substantially stationary (e.g., such that it atmost undergoes pendulum and/or circular movement about the firstposition); (ii) translating the first energy beam to a second positionon the target surface along the path-of-tiles, which second position isdifferent from the first position, wherein the first energy beam istranslated during an intermission without transforming thepre-transformed material along the path-of-tiles; and (iii) using thefirst energy beam during a second time period to form a second tilealong the path-of-tiles, wherein during the second time period, thefirst energy beam is stationary or substantially stationary (e,g, suchthat it at most undergoes pendulum and/or circular movement about thesecond position). In some embodiments, forming the plurality of tilescomprises moving the first energy beam to a subsequent location of thepre-transformed material (e.g., subsequent location of the exposedsurface of the material bed) along a path. In some embodiments, formingthe plurality of tiles comprises repeating (ii) and (iii) to an end ofthe path-of-tiles. In some embodiments, the method further comprises:reducing a power of an energy source that generates the first energybeam during movement of the first energy beam during an intermissionbetween irradiating the different locations such that during theintermission the energy beam does not transform the pre-transformedmaterial. In some embodiments, reducing comprising turning off. In someembodiments, during an irradiation time of the first energy beam and/orof the second energy beam, a power density profile of the first energybeam comprises a period in which the power density profile of the firstenergy beam is decreasing. In some embodiments, the period in which thepower density profile of the first energy beam is decreasing occurs atan end of the irradiation time. In some embodiments, during anirradiation time of the first energy beam, a power density of the firstenergy beam is constant. In some embodiments, (a) and/or (b) comprisesforming a plurality of hatches by continuously moving the first energybeam along the pre-transformed material in accordance with a path. Insome embodiments, the first energy beam emits continuous or intermittent(e.g., pulsing) irradiation. In some embodiments, the one or more layersof transformed material printed in (a) comprise one or more poresdisposed asymmetrically within a height of a layer of the one or morelayers relative to a midline of the layer height. In some embodiments,the one or more pores that are disposed asymmetrically within a heightof a layer of the one or more layers, are disposed asymmetrically belowthe midline of the layer. In some embodiments, the pore is disposed at alocation deeper than the height of two layers of the one or more layers(e.g., deeper than six layers of the one or more layers).

In another aspect, printing a three-dimensional object comprises one ormore controllers that are individually or collectively programmed to:(a) direct a first energy beam to transform one or more layers ofpre-transformed material to one or more layers of transformed material;and (b) direct a second energy beam that reduces a porosity of the oneor more layers of transformed material, wherein reducing the porositycomprises transforming at least a portion of the one or more layers oftransformed material.

In some embodiments, the one or more controllers are individually orcollectively programmed to direct (i) a first energy source to generatethe first energy beam, and (ii) direct a second energy source togenerate the second energy beam. In some embodiments, the first energysource is the same as the second energy source. In some embodiments, thefirst energy source is different than the second energy source. In someembodiments, the one or more controllers controls at least onecharacteristic of the first energy beam, the second energy beam, thefirst energy source, and/or the second energy source. In someembodiments, the one or more controllers controls at least onecharacteristic of the first and/or second energy beams at leastpartially based on data from one or more sensors. In some embodiments,the one or more sensors collect temperature, optical, or spectroscopicdata. In some embodiments, the one or more sensors detectelectromagnetic radiation that is emitted and/or reflected from anexposed surface of one or more melt pools formed during directing thefirst energy beam in (a) and/or directing the second energy beam in (b).In some embodiments, directing the first energy beam in (a) and/ordirecting the second energy beam in (b) comprises forming a bottom skinof an overhang. In some embodiments, the one or more controllerscontrols at least one characteristic of the first energy beam and/or thesecond energy beam at least partially based on monitoring a plasticyielding of the bottom skin during printing. In some embodiments, theone or more controllers directs feedback or closed loop control. In someembodiments, the one or more controllers directs feed-forward or openloop control. In some embodiments, the one or more controllers isprogrammed to direct the same energy source to generate the first andsecond energy beams. In some embodiments, the one or more controllers isprogrammed to direct different energy sources to generate the first andsecond energy beams. In some embodiments, the one or more controllersincludes at least two controllers. In some embodiments, one of the atleast two controllers is programmed to direct the first energy beam in(a) and/or directing the second energy beam in (b). In some embodiments,at least two of the at least two controllers is programmed to direct thefirst energy beam in (a) and/or directing the second energy beam in (b).In some embodiments, the one or more controllers is programmed to adjustat least one characteristic of the first energy beam and/or the secondenergy beam to he different from each other. In some embodiments, the atleast one characteristic comprises a speed, a power density, a crosssection, a dwell time, or a propagation scheme. In some embodiments, thepropagation scheme comprises hatching or tiling. In some embodiments,hatching comprises transformation during a movement. In someembodiments, tiling comprises (I) transforming while being stationary orsubstantially stationary (e.g., about a first point along a path)followed by (II) propagating along a path to a second point withouttransforming and (III) repeating (I) and (II) until reaching an end ofthe path. In some embodiments, the one or more controllers is programmedto direct the first and second energy beams to have different powerdensities. In some embodiments, a power density of the second energybeam is greater than a power density of the first energy beam. In someembodiments, a power density of the second energy beam is less than apower density of the first energy beam. In some embodiments, the one ormore controllers is programmed to direct the first energy beam to scanat a first speed, and to direct the second energy beam to scan at asecond speed different than the first speed. In some embodiments, thesecond speed is faster than the first speed. In some embodiments, thesecond speed is slower than the first speed. In some embodiments, theone or more controllers is programmed to direct the first energy beamand/or the second energy beam to form a plurality of tiles. In someembodiments, each tile of the plurality of tiles is formed by directingthe first energy beam at the one or more layers of pre-transformedmaterial for a dwell time of at least about 0.1 milliseconds during astationary or substantially stationary irradiation (e.g., about a pointalong a path). In some embodiments, the one or more controllers isprogrammed to direct an energy source to form a plurality of hatches bycontinuously moving the first energy beam along the one or more layersof pre-transformed material in accordance with a path. In someembodiments, the one or more controllers is programmed to direct thesecond energy beam to form at least one high aspect ratio melt pool. Insome embodiments, a depth of the at least one high aspect ratio meltpool is greater than a radius of an exposed surface of the at least onehigh aspect ratio melt pool. In some embodiments, the depth is at leasttwice the radius of the exposed surface of the high aspect ratio meltpool. In some embodiments, the one or more controllers is programmed todirect the second energy beam to reduce a volume percentage porosityand/or an area percentage porosity of the transformed material by atleast about one order of magnitude. In some embodiments, the one or morecontrollers is programmed to direct adjusting one or morecharacteristics of the first and/or second energy beams before, duringor after directing the first energy beam in (a) and/or directing thesecond energy beam in (b). In some embodiments, the at least onecharacteristic of the first and/or second energy beams is adjusted toaccomplish a different solidification rate during directing the firstenergy beam in (a) and/or directing the second energy beam in (b). Insome embodiments, the one or more controllers is programmed to directthe second energy beam to form a melt pool comprising a well in acentral region of the melt pool. In some embodiments, directing thesecond energy beam in (b) further comprises laterally elongating thewell by laterally moving the second energy beam along a path. In someembodiments, the one or more controllers is programmed to direct (e,g,gradually) lowering an intensity of the second energy beam duringformation of the melt pool comprising the well and/or during the lateralmovement to allow closure of the well. In some embodiments, using thesecond energy beam to reduce the porosity comprises alters amicrostructure of the or more layers of transformed material. In someembodiments, the one or more controllers is programmed to direct thesecond energy beam to increase a density of the or more or more layersof transformed material by at least about 85%, 95.5% or 110% whichpercentage is a volume per volume percentage and/or an area per areapercentage. In some embodiments, the one or more controllers isprogrammed to direct using a tiling energy beam during directing thefirst energy beam in (a) and/or during directing the second energy beamin (b). In some embodiments, tiling comprises (1) irradiating a firstposition along a path with a stationary or substantially stationaryenergy beam to perform a first transformation directly followed by (2)propagation along the path without transformation, directly followed by(3) repeating (1) and (2) until reaching an end of the path.

In another aspect, a method of printing a three-dimensional objectcomprises: (a) providing a first layer of pre-transformed material abovea platform; (b) using a first energy beam to transform at least aportion of the first layer of pre-transformed material to a first porouslayer comprising a first portion and an optional second portion; and (c)using a second energy beam to densify the at least the first portion ofthe first porous layer to form a first layer of denser material that isdenser than the first porous layer, wherein the optional second portionis not at least a portion of a scaffold that engulfs thethree-dimensional object.

In some embodiments, the scaffold is a lightly sintered pre-transformedmaterial. In some embodiments, the first porous layer is suspendedanchorlessly within an enclosure. In some embodiments, the first porouslayer is suspended anchorlessly within an enclosure (e.g., wherein thefirst porous layer is anchored to the enclosure). In some embodiments,the first porous layer is suspended anchorlessly within an enclosure(e.g., wherein the first porous layer is anchored to a platform abovewhich the first layer of pre-transformed material is disposed in theenclosure). In some embodiments, the first porous layer is directlyconnected to the platform. In some embodiments, the first porous layeris connected to the platform through one or more auxiliary supports. Insome embodiments, the first portion and an optional second portion ofthe first porous layer are transformed to form the first layer of densermaterial in operation (c). In some embodiments, transforming comprisesfusing. In some embodiments, fusing comprises sintering or inciting. Insome embodiments, melting comprises completely melting. In someembodiments, the first porous layer is suspended anchorlessly within anenclosure. In some embodiments, the first porous layer has a porosity ofat least 40%. In some embodiments, the first porous layer has a porosityof at least 60%. In some embodiments, the first porous layer has aporosity of at least 20%. In some embodiments, a surface of the firstlayer of denser material has an arithmetic average roughness profile(Ra) of at most 200 micrometers. In some embodiments, the first layer ofdenser material has an average radius of curvature of at least fivecentimeters. In some embodiments, the first layer of denser material hasan average radius of curvature of at least 50 centimeters. In someembodiments, the first layer of denser material has an average radius ofcurvature of at least one meter. In some embodiments, the first layer ofpre-transformed material is selected from at least one member of thegroup consisting of an elemental metal, metal alloy, ceramic, anallotrope of elemental carbon polymer, and resin. In some embodiments,the first layer of pre-transformed material comprises a liquid, solid,or semi-solid. In some embodiments, the first layer of pre-transformedmaterial comprises a particulate material. In some embodiments, theparticulate material comprises powder. In some embodiments, the powdercomprises solid particles. In some embodiments, the first porous layercomprises one or more pores. In some embodiments, the one or more porescomprises a pore structure. In some embodiments, the pore structurecomprises pores distributed in a non-uniform manner across the firstporous layer. In some embodiments, the pore structure comprises poresdistributed in a uniform manner across the first porous layer. In someembodiments, the first layer of pre-transformed material forms amaterial bed that is at an ambient temperature during the printing. Insome embodiments, the first layer of pre-transformed material forms amaterial bed that is at an ambient pressure during the printing. In someembodiments, the first layer of pre-transformed material forms amaterial bed, and wherein during the printing, the material bed is at aconstant or at a substantially constant pressure. In some embodiments,the first layer of pre-transformed material forms a material bed, andwherein during the printing the material bed is devoid of a substantialpressure gradient. In some embodiments, the first layer ofpre-transformed material comprises a particulate material. In someembodiments, the first layer of pre-transformed material comprises apowder material. In some embodiments, the first energy beam and/or thesecond energy beam is pulsing during the printing. In some embodiments,the first energy beam and/or the second energy beam is continuous duringthe printing. In some embodiments, during the printing, the first energybeam and/or the second energy beam has a constant characteristiccomprising a velocity, a continuity of movement, a cross section, apower density, a fluence, a duty cycle, a dwell time, a focus, or adelay time. In some embodiments, during the printing, the first energybeam and/or the second energy beam has a varied characteristiccomprising a velocity, a continuity of movement, a cross section, apower density, a fluence, a duty cycle, a dwell time, a focus, or adelay time. In some embodiments, the first layer of pre-transformedmaterial forms a material bed, wherein during the delay time the firstenergy beam and/or the second energy beam is translated from a firstposition of an exposed surface of the material bed to a second positionof the exposed surface of the material bed. In some embodiments, duringthe printing comprises during operation (b) or during operation (c). Insome embodiments, the varied characteristic is controlled in real timeby a controller. In some embodiments, during the printing the firstenergy beam and/or the second energy beam is dithering. In someembodiments, during the printing the first energy beam and/or the secondenergy beam has a circular footprint. In some embodiments, during theprinting the first energy beam and/or the second energy beam has an ovalfootprint. In some embodiments, the first layer of pre-transformedmaterial forms a material bed, wherein in operation (b), operation (c),or both in operations (b) and (c): a trajectory of the first energy beamand/or a second energy beam on an exposed surface of the material bedcomprises vectoral sections that collectively propagate in a firstdirection, (e.g., wherein the vectoral sections are directed in a seconddirection that is different from the first direction, wherein the firstdirection is a direction of growth of the first porous layer and/or thefirst layer of denser material, or any combination thereof). In someembodiments, the first energy beam and/or the second energy beam istranslated along a trajectory. In some embodiments, the trajectorycomprises translating in a back and forth motion (e.g., like apendulum). In some embodiments, transforming comprises forming a meltpool. In some embodiments, using the second energy beam to densify theat least the first portion of the first porous layer comprises forming amelt pool having an aspect ratio. In some embodiments, the aspect ratiois a ratio of a depth of the melt pool to a width (e.g., diameter) of anexposed surface of the melt pool in at least one vertical cross section.In some embodiments, the aspect ratio is a ratio of a depth of the meltpool to a melt pool width at an exposed surface of at least one verticalcross section of the melt pool. In some embodiments, the melt pool has alow aspect ratio. In some embodiments, a low aspect ratio is when thedepth of the melt pool is shorter than a width (e.g., diameter) of anexposed surface of the melt pool in at least one vertical cross section.In some embodiments, the melt pool has a high aspect ratio, wherein thedepth of the melt pool is larger than a width of the exposed surface ofthe melt pool in at least one vertical cross section of the melt pool.In some embodiments, the melt pool is hemispherical or substantiallyhemispherical, wherein the depth of the melt pool is equal orsubstantially equal to half of the width (e.g., a radius) of an exposedsurface of the melt pool in at least one vertical cross section of themelt pool. In some embodiments, forming the melt pool includes using thesecond energy beam to irradiate in one or more welding modes thatcomprise a conduction, transition keyhole, penetration keyhole, ordrilling. In some embodiments, the method further comprises afteroperation (b): (i) providing a second layer of pre-transformed materialabove a platform and (ii) using an energy beam to transform at least aportion of the second layer of pre-transformed material to form asecond, porous layer comprising a first portion of the second porouslayer and an optional second portion of the second porous layer. In someembodiments, the method further comprises before operation (c): (i)providing a second layer of pre-transformed material above a platformand (ii) using an energy beam to transform at least a portion of thesecond layer of pre-transformed material to form a second porous layercomprising a first portion of the second porous layer and an optionalsecond portion of the second porous layer. In some embodiments, themethod further comprises using the second energy beam to densify thefirst portion of the second porous layer to form a second layer ofdenser material as compared to the first portion of the second porouslayer, as a part of the three-dimensional object, wherein the optionalsecond portion of the second porous layer is not at least a portion of ascaffold that engulfs the three-dimensional object. In some embodiments,in operation (c) the second energy beam densifies the first portion ofthe first porous layer and the first portion of the second porous layerto form a first layer of denser material and a second layer of densermaterial, and wherein the first layer of denser material and the secondlayer of denser material are the same layer. In some embodiments, thefirst layer of denser material is different from the second layer ofdenser material. In some embodiments, operation (b) is after operation(c). In some embodiments, the second porous layer has a porosity of atleast 40%. In some embodiments, the second porous layer has a porosityof at least 60%. In some embodiments, the second porous layer has aporosity of at least 20%. In some embodiments, a surface of the secondlayer of denser material has an arithmetic average of a roughnessprofile (Ra) of at most 200 micrometers. In some embodiments, the secondlayer of denser material has an average radius of curvature of at leastfive centimeters. In some embodiments, the second layer of densermaterial has an average radius of curvature of at least 50 centimeters.In some embodiments, the second layer of denser material has an averageradius of curvature of at least one meter. In some embodiments, thesecond porous layer comprises one or more pores. In some embodiments,the one or more pores comprises a pore structure. In some embodiments,the pore structure comprises pores distributed in a non-uniform manneracross the second porous layer. In some embodiments, the pore structurecomprises pores distributed in a uniform or substantially uniform manneracross the second porous layer. In some embodiments, the first layer ofpre-transformed material is sandwiched between the first porous layerand the second porous layer. In some embodiments, a porosity of thefirst porous layer is different than a porosity of the second porouslayer. In some embodiments, a porosity of the first porous layer is sameas a porosity of the second porous layer. In some embodiments, the firstenergy beam is a type-2 energy beam (e.g., as disclosed herein). In someembodiments, the first energy beam is a type-1 energy beam (e.g., asdisclosed herein). In some embodiments, the type-2 energy beam issubstantially stationary. In some embodiments, the type-1 energy beam istranslating. In some embodiments, the first portion of the first porouslayer and the first portion of the second porous layer are densifiedusing the same energy beam. In some embodiments, the first portion ofthe first porous layer and the first portion of the second porous layerare densified using different energy beams. In some embodiments, thefirst energy beam used to density the first portion of the first porouslayer has at least one characteristic that is different than acharacteristic of the second energy beam used to densify the secondporous layer.

In another aspect, a system for printing at least one three-dimensionalobject comprises: an enclosure that is configured to accommodate amaterial bed that comprises a pre-transformed material; a first energysource that is configured to generate a first energy beam thattransforms a portion of the pre-transformed material to form a part ofthe at least one three-dimensional object; a second energy source thatis configured to generate a second energy beam that transforms a portionof the pre-transformed material to form a part of the at least onethree-dimensional object; and at least one controller that is configuredto direct the first energy beam and time second energy beam, which atleast one controller is collectively or separately programmed to directperformance of the following operations: operation (i) direct the firstenergy beam to transform the portion of the pre-transformed material toform a porous layer comprising a first portion and an optional secondportion and operation (ii) direct the second energy beam to transformand thereby densify the first portion of the porous layer to form adenser layer, wherein the optional second portion does not engulf thefirst portion.

In some embodiments, time first energy beam and/or second energy beamcomprises an electromagnetic or charged particle beam. In someembodiments, the first energy beam comprises a laser beam. In someembodiments, the porous layer is a first porous layer, wherein the atleast one controller is programmed to perform the following operationsafter operation (ii): operation (I) direct providing a second layer ofpre-transformed material above a platform and (II) direct the firstenergy beam to transform at least a portion of the second layer ofpre-transformed material to form a second porous layer comprising afirst portion of the second porous layer and an optional second portionof the second porous layer. In some embodiments, the porous layer is afirst porous layer, wherein the at least one controller is programmed toperform the following operations before operation (ii): operation (I)direct providing a second layer of pre-transformed material above aplatform and (II) direct the first energy beam to transform at least aportion of the second layer of pre-transformed material to form a secondporous layer comprising a first portion of the second porous layer andan optional second portion of the second porous layer. In someembodiments, the at least one controller is programmed to direct thesecond energy beam to densify the first portion of the second porouslayer to form a second denser layer as compared to the first portion ofthe second porous layer, which second denser layer forms a part of theat least one three-dimensional object, wherein the second portion of thesecond porous layer is not at least a portion of a scaffold that engulfsthe at least one three-dimensional object. In some embodiments, time atleast one controller is programmed to perform the following operationsin operation (ii): direct the second energy beam to densify the firstportion of the first porous layer when densifying the first portion ofthe second porous layer to form the first denser layer, and wherein thefirst denser layer and the second denser layer are the same. In someembodiments, the first denser layer is different from the second denserlayer. In some embodiments, after operation (i) is after operation (ii).

In another aspect, an apparatus for three-dimensional printing of atleast one three-dimensional object comprises at least one controllerthat is programmed to perform the following operations: operation (a)provide pre-transformed material to form a material bed, operation (b)direct a first energy beam to transform a portion of material bed toform a porous layer that comprises a first portion and an optionalsecond portion, wherein the first energy beam is operatively coupled tothe material bed; and operation (c) direct a second energy beam, to densa first portion of the porous layer to form a layer of denser materialas a part of the at least one three-dimensional object.

In some embodiments, the at least one controller is a multiplicity ofcontrollers and wherein at least two of operation (a), operation (b),and operation (c) are directed by the same controller. In someembodiments, the at least one controller is a multiplicity ofcontrollers and wherein at least two of operation (a), operation (b),and operation (c) are directed by different controllers.

In another aspect, a computer software product for three-dimensionalprinting of at least one three-dimensional object, comprises anon-transitory computer-readable medium in which program instructionsare stored, which instructions, when read by a computer, cause thecomputer to perform operations comprising: operation (a) directproviding a pre-transformed material to form a material bed; operation(b) directing a first energy beam to transform a portion of thepre-transformed material to form a porous layer comprising a firstportion and an optional second portion, wherein the first energy beam isoperatively coupled to the material bed; and operation (c) directing asecond energy beam, to densify the first portion of the porous layer toform a layer of denser material as a part of the at least onethree-dimensional object.

In another aspect, printing a three-dimensional object comprises: (a)transforming a first pre-transformed material to a first transformedmaterial to print one or more layers of hardened material as part of thethree-dimensional object that is printed layerwise, which one or morelayers define a layering plane indicative (e.g., characteristic, ortypical) of the layerwise printing of the three-dimensional object; (b)transforming a second pre-transformed material to a second transformedmaterial to print at least a portion of an overhang of thethree-dimensional object, wherein a vector normal to a surface at apoint on an exterior surface of the overhang that intersects (i) thelayering plane or (ii) a plane parallel to the layering plane, forms anangle with respect to the layering plane, which second transformedmaterial comprises a porous matrix; and (c) using an energy beam todensify the second transformed material.

In some embodiments, the one or more layers defines a Z vectorindicative (e.g., characteristic, or typical) of a direction of thelayerwise printing of the three-dimensional object. In some embodiments,the Z vector is perpendicular to the layering plane. In someembodiments, the angle is at least about sixty degrees and at most aboutninety degrees with respect to (i) the layering plane that intersectsthe vector or to (ii) the plane parallel to the layering plane thatintersects the vector, which vector is directed towards (e.g., into) thesecond transformed material. In some embodiments, the angle is at leastabout seventy degrees and at most about ninety degrees with respect to(i) the layering plane that intersects the vector or to (ii) the planeparallel to the layering plane that intersects the vector, which vectoris directed towards the second transformed material. In someembodiments, the non-perpendicular angle is at least about eightydegrees and at most about ninety degrees with respect to (i) thelayering plane that intersects the vector or to (ii) the plane parallelto the layering plane that intersects the vector, which vector isdirected towards the second transformed material. In some embodiments,using the energy beam to densify comprises altering a microstructure ofthe first transformed material to form the second transformed material.In some embodiments, the porous matrix comprises at least one pore. Insome embodiments, (c) comprises forming a high aspect ratio melt pool.In some embodiments, a depth of the high aspect ratio melt pool isgreater than a radius of an exposed surface of the high aspect ratiomelt pool. In some embodiments, the depth is at least twice the radiusof the exposed surface of the high aspect ratio melt pool. In someembodiments, (c) comprises reducing a volume percentage and/or an areapercentage porosity of the second transformed material by at least aboutone order of magnitude. In some embodiments. (c) comprises reducing anarea percentage porosity of the second transformed material by at leastabout one order of magnitude. In some embodiments, the secondtransformed material comprises a plurality of layers. In someembodiments, (c) comprises transforming at least a fraction of each ofthe plurality of layers. In some embodiments, (c) comprises using awelding process. In some embodiments, the welding process comprises(e.g., completely) melting at least a fraction of the second transformedmaterial. In some embodiments, the second transformed materialcorresponds to at least a portion of a skin of the three-dimensionalobject. In some embodiments, the skin is a bottom skin of the overhang.In some embodiments, the bottom skin has an area surface roughness (Sa)of at most about 100 micrometers. In some embodiments, the bottom skinhas an area surface roughness (Sa) of at most about 50 micrometers. Insome embodiments, the porous matrix in (b) forms a bottom skin of theoverhang. In some embodiments, densification in (c) comprises directingthe energy beam in accordance with a path along or parallel to an edgeof the first transformed material. In some embodiments, the energy beamin (c) is a second energy beam. In some embodiments, (b) comprisesgenerating a first energy beam from a first energy source. In someembodiments, (c) comprises generating the second energy beam from asecond energy source. In some embodiments, the first energy source isthe same as the second energy source. In some embodiments, the firstenergy source is different than the second energy source. In someembodiments, the energy beam in (c) is a third energy beam, wherein themethod further comprises using a first energy beam to transform thefirst pre-transformed material in (a), using a second energy beam totransform the second pre-transformed material in (b), and wherein (i)the first energy beam, the second energy beam, and/or the third energybeam follow a hatching propagation scheme. In some embodiments, thehatching propagation scheme comprises transforming while translatingalong a path. In some embodiments, the energy beam in (c) is a thirdenergy beam, wherein the method further comprises using a first energybeam to transform the first pre-transformed material in (a), using asecond energy beam to transform the second pre-transformed, material in(b), and wherein (i) the first energy beam, the second energy beam,and/or the third energy beam follow a tiling propagation scheme. In someembodiments, the tiling propagation scheme comprises (I) transformingwhile being stationary or substantially stationary (e.g., about a, firstpoint along a path) followed, by (II) propagating along the path to asecond point without transforming and (III) repeating (I) and (II) untilreaching an end of the path. In some embodiments, substantiallystationary comprises a movement (e.g., that does not exceed afundamental length scale of a footprint of the energy beam on the secondpre-transformed material). The substantially stationary movement may beabout a point in a pendulum and/or in a circular motion. In someembodiments, the tiling propagation scheme comprises: (i) transformingthe first pre-transformed material to the first transformed material ata first position on a target surface using the energy beam during afirst time period to form a first tile, which first position is along apath-of-tiles, wherein during the first time period, the energy beam isstationary or substantially stationary (e.g., such that it at mostundergoes a pendulum and/or a circular movement about the firstposition); (ii) translating the energy beam to a second position on thetarget surface along the path-of-tiles, which second position isdifferent from the first position, wherein the energy beam is translatedduring an intermission without transforming the pre-transformed materialalong the path-of-tiles; and (iii) using the energy beam during a secondtime period to form a second tile along the path-of-tiles, whereinduring the second time period, the energy beam is stationary orsubstantially stationary (e.g., such that it at most undergoes thependulum and/or the circular movement about the second position). Insome embodiments, the energy beam in (c) is a tiling energy beam. Insome embodiments, a spot size of a hatching energy beam is smaller thana spot size of the tiling energy beam. In some embodiments, (c)comprises forming a plurality of tiles. In some embodiments, each tileis formed by directing the energy beam at the second pre-transformedmaterial for a dwell time of at least about 0.1 milliseconds. In some,embodiments, the dwell time is at least about 10 milliseconds. In someembodiments, the energy beam is substantially stationary during thedwell time. In some embodiments, substantially stationary comprises amovement that does not exceed a fundamental length scale of a footprintof the energy beam on the second pre-transformed material. Thesubstantially stationary movement may be about a point in a pendulumand/or in a circular motion. In some embodiments, (c) comprises forminga plurality of tiles by: (i) transforming the first pre-transformedmaterial to the first transformed material at a first position on atarget surface using the energy beam during a first time period to forma first tile, which first position is along a path-of-tiles, whereinduring the first time period, the energy beam is stationary orsubstantially stationary (e.g., such that it at most undergoes apendulum and/or a circular movement about the first position); (ii)translating the energy beam to a second position on the target surfacealong the path-of-tiles, which second position is different from thefirst position, wherein the energy beam is translated during anintermission without transforming the first pre-transformed materialalong the path-of-tiles; and (iii) using the energy beam during a secondtime period to form a second tile along the path-of-tiles, whereinduring the second time period, the energy beam is stationary orsubstantially stationary (e.g., such that it at most undergoes thependulum and/or the circular movement about the second position). Insome embodiments, forming the plurality of tiles comprises moving theenergy beam on the second pre-transformed material in accordance with apath to form a path of tiles. In some embodiments. (b) comprises forminga plurality of layers of the porous matrix. In some embodiments, theenergy beam in (c) is a second energy beam. In some embodiments, formingthe plurality of layers of the porous matrix comprises using a firstenergy beam. In some embodiments, the energy beam in (c) is a thirdenergy beam. In some embodiments, (v) comprises forming a first of theplurality of layers of the porous matrix comprises using a first energybeam and forming a second of the plurality of layers of the porousmatrix using a second energy beam. In some embodiments, a power densityof the first energy beam differs that a power density of the secondenergy beam. In some, embodiments. (c) comprises transforming aplurality of layers of the porous matrix. In some embodiments, (c)comprises transforming a plurality of layers of the porous matrix andone or more intervening layers of pre-transformed material. In someembodiments, the transforming in (a) is with a first energy beam, thetransforming in (b) is with a second energy beam, and the transformingin (c) is with a third energy beam. In some embodiments, at least two ofthe first energy beam, the second energy beam, and the third energy beamare generated with the same energy source. In some embodiments, thetransforming in (a) is with a first energy beam, the transforming in (b)is with a second energy beam, the transforming in (c) is with a thirdenergy beam, wherein at least two of the first energy beam, the secondenergy beam, and the third energy beam are generated with differentenergy sources. In some embodiments, the transforming in (a) is with afirst energy beam, the transforming in (b) is with a second energy beam,the transforming in (c) is with a third energy beam, wherein at leasttwo of the first energy beam, the second energy beam, and the thirdenergy beam have at least one energy beam characteristic that is thesame. In some embodiments, the transforming in (a) is with a firstenergy beam, the transforming in (b) is with a second energy beam, thetransforming in (c) is with a third energy beam, wherein at least two ofthe first energy beam, the second energy beam, and the third energy beamhave at least one different energy beam characteristic. In someembodiments, the at least one different energy beam characteristiccomprises wavelength, cross-section, speed, power density, or focalpoint. In some embodiments, the second transformed material has ahorizontally non-overlapping portion with respect to the firsttransformed material.

In another aspect, printing a three-dimensional object comprises one ormore controllers that are individually or collectively programmed to:(a) direct transforming a first pre-transformed material to a firsttransformed material to print one or more layers of hardened material aspart of the three-dimensional object that is printed layerwise, whichone or more layers define a layering plane indicative (e.g.,characteristic, or typical) of a layerwise printing of thethree-dimensional object; (b) direct transforming a secondpre-transformed material to a second transformed material to print atleast a portion of an overhang of the three-dimensional object, whereina vector normal to a surface at a point on an exterior surface of theoverhang that intersects (i) the layering plane that or (ii) a planeparallel to the layering plane, forms an angle with respect to thelayering plane, which second transformed material comprises a porousmatrix; and (c) direct an energy beam to densify the second transformedmaterial.

In some embodiments, at least two of (a), (b) and (c) are directed bythe same controller of the one or more controllers. In some embodiments,at least two of (a), (b) and (c) are directed by different controllersof the one or more contracts. In some embodiments, the one or morecontrollers is programed to direct: (I) a first energy source togenerate a first energy beam for transforming in (b), and (II) a secondenergy source to generate a second energy beam for densifying in (c). Insome embodiments, the first and second energy sources are the same. Insome embodiments, the first and second energy sources are different. Insome embodiments, the one or more controllers controls at least onecharacteristic of the energy beam or of an energy source that generatesthe energy beam. In some embodiments, the energy beam is a second energybeam. In some embodiments, direct transforming the secondpre-transformed material in (b) is by directing a first energy beam totransforming the second pre-transformed material. In some embodiments,the energy beam is a third energy beam. In some embodiments, directtransforming the first pre-transformed material in (a) is by directing afirst energy beam to transform the first pre-transformed material. Insome embodiments, direct transforming the second pre-transformedmaterial in (b) is by directing a second energy beam to transform thesecond pre-transformed material. In some embodiments, at least two ofthe first energy beam, the second energy beam and the third energy beamare the same. In some embodiments, at least two of the first energybeam, the second energy beam and the third energy beam are differentenergy beams. In some embodiments, the one or more controllers furtherdirects: a first energy source to generate the first energy beam, asecond energy source to generate the second energy beam, a third energysource to generate the third energy beam. In some embodiments, at leasttwo of the first energy source, the second energy source and the thirdenergy source are different energy sources. In some embodiments, atleast two of the first energy source, the second energy source and thethird energy source is the same energy source. In some embodiments, atleast two of the first energy beam, the second energy beam and the thirdenergy beam are different energy beams. In some embodiments, the one ormore controllers controls at least one characteristic of the firstenergy beam and/or the second energy beam at least partially based ondata from one or more sensors. In some embodiments, the one or moresensors collect temperature, optical, or spectroscopic data. In someembodiments, the one or more sensors detect electromagnetic radiationthat is emitted and/or reflected from an exposed surface of one or moremelt pools formed during transformation in (a), (b) and/or (c). In someembodiments, the energy beam in (c) is a second energy beam. In someembodiments. (b) comprises using a first energy beam, wherein (b) and/or(c) comprise forming a bottom skin of the overhang. In some embodiments,the one or more controllers controls at least one characteristic of thefirst energy beam and/or the second energy beam at least partially basedon monitoring a plastic yielding of the bottom skin during printing. Insome embodiments, the one or more controllers include a control schemecomprising feedback, or closed loop. In some embodiments, the one ormore controllers include a control scheme comprising feed-forward oropen loop control. In some embodiments, the one or more controllers isprogrammed to direct forming a high aspect ratio melt pool during (c).In some embodiments, a depth of the high aspect ratio melt pool isgreater than a width of the high aspect ratio melt pool. In someembodiments, the second transformed material comprises a plurality oflayers. In some embodiments, the one or more controllers is programmedto direct transforming at least a fraction of each of the plurality oflayers during densification in (c). In some embodiments, the firsttransformed material comprises an edge. In some embodiments, the one ormore controllers is programmed to direct the energy beam in accordancewith a path along the edge or parallel to the edge (e.g., and away fromthe first transformed material). In some embodiments, the one or morecontrollers is programmed to direct the energy beam to propagate via ahatching propagation scheme. In some embodiments, the hatchingpropagation scheme comprises continuous irradiation during propagationof the energy along a path to perform a transformation. In someembodiments, the one or more controllers is programmed to (i) direct thefirst energy beam, the second energy beam and/or the third energy beamto propagate via tiling propagation scheme. In some embodiments, tilingcomprises (I) irradiating a first position along a path with astationary or substantially stationary energy beam to perform a firsttransformation directly followed by (2) propagation along the pathwithout transformation, directly followed by (3) repeating (1) and (2)until reaching an end of the path. In some embodiments, substantiallystationary is a pendulum and/or rotational movement about a point alongthe path. In some embodiments, the movement is of a length scale of atmost a cross section and/or an irradiation spot of the energy beam. Insome embodiments, the one or more controllers is programmed to directusing a hatching energy beam during (b) and a tiling energy beam during(c). In some embodiments, a spot size anchor a cross section of thehatching energy beam is smaller than a spot size and/or a cross sectionof the tiling energy beam respectively. In some embodiments, the one ormore controllers is programmed to direct forming a plurality of tilesduring (c). In some embodiments, each tile is formed by directing theenergy beam at the second pre-transformed material for a dwell time ofat least about 0.3 milliseconds. In some embodiments, the dwell time isat least about 10 milliseconds. In some embodiments, the energy beam issubstantially stationary during the dwell time. In some embodiments,substantially stationary comprises movement about a point that does notexceed a fundamental length scale of a footprint of the energy beam onthe second pre-transformed material. In some embodiments, the one ormore controllers is programmed to direct moving the energy beam todifferent locations of the second pre-transformed material in accordancewith a path. In some embodiments, the one or more controllers isprogrammed to direct forming a plurality of layers of the porous matrixduring (b). In some embodiments, (b) comprises directing the energy beamto transform the second pre-transformed material to the secondtransformed material. In some embodiments, the one or more controllersthat is programed to direct adjusting one or more characteristics of theenergy beam before and/or daring (c). In some embodiments, the one ormore characteristics of the energy beam is adjusted to accomplish adifferent solidification rate during (c) as compared to during (b). Insome embodiments, the one or more controllers is programmed to direct(b) such that the second transformed material has a horizontallynon-overlapping portion with respect to the first transformed material.

In another aspect, a method of printing a three-dimensional objectcomprises: (a) providing a material bed that comprises a pre-transformedmaterial and a first hard material that is a first segment of thethree-dimensional object; (b) using a first energy beam to transform aportion of the pre-transformed material to a form a porous layer,wherein the porous layer is connected to the first hard material and hasa horizontally non-overlapping portion with the first hard material,which first transformed material is formed anchorlessly within anenclosure; and. (c) using a second energy beam to transform at least aportion of the porous layer to form a first denser layer that isconnected to the first hard material to form at least a second segmentof the three-dimensional object that includes the first segment.

In some embodiments, the first hard material is suspended anchorlesslyin an enclosure during the printing. In some embodiments, the first hardmaterial is anchored to the enclosure during the printing. In someembodiments, anchored is directly anchored to a base above which thematerial bed is disposed. In some embodiments, anchored comprisesanchored through one or more auxiliary supports. In some embodiments,the horizontally non-overlapping portion forms at least a segment of anoverhang or a cavity ceiling. In some embodiments, the overhang or thecavity ceiling form an angle with an exposed surface of the material bedand/or with a platform above which the material bed is disposed, whereinthe angle is from zero to thirty degrees. In some embodiments, the angleis from zero to fifteen degrees. In some embodiments, the horizontallynon-overlapping portion comprises a bottom skin surface that faces aplatform above which the material bed is disposed. In some embodiments,the bottom skin surface has an arithmetic average of a roughness profileof at most 200 micrometers. In some embodiments, the first denser layerhas an average radius of curvature of at least five centimeters. In someembodiments, the first denser layer has an average radius of curvatureof at least 50 centimeters. In some embodiments, the first denser layerhas an average radius of curvature of at least one meter. In someembodiments, the method further comprises (i) providing a layer ofpre-transformed material adjacent to the first denser layer, (ii) usingthe first energy beam to transform a portion of the layer ofpre-transformed material to form a second porous layer, wherein thesecond porous layer is connected to the first denser layer, and (iii)using the second energy beam to densify at least a portion of the secondporous layer to form a second denser layer as a part of thethree-dimensional object. In some embodiments, the first energy beam isa type-2 energy beam. In some embodiments, the first hard material is arigid portion of the three-dimensional object. In some embodiments,after its formation, the rigid portion experiences insignificantdeformation at least during the printing. In some embodiments, after itsformation, the rigid portion is resistant or substantially resistant todeformation at least during the printing. In some embodiments, after itsformation, the rigid portion is resistant or substantially resistant todeformation, wherein the deformation comprises stress. In someembodiments, after its formation, the rigid portion does formsignificant defects at least during the printing. In some embodiments,the defects comprise structural defects. In some embodiments, thedefects comprise a crack, ball, droop, or dislocation.

In another aspect, a system for printing at least one three-dimensionalobject comprises: an enclosure that is configured to accommodate amaterial bed that comprises a pre-transformed material and a hardmaterial that is a first segment of the at least one three-dimensionalobject; an energy source that is configured to generate an energy beamthat transforms a portion of the pre-transformed material to a form asecond segment of the at least one three-dimensional object, wherein theenergy beam is operatively coupled to the enclosure; and at least onecontroller that is configured to direct the energy beam, which the atleast one controller is collectively or separately programmed to performthe following operations: (i) direct the energy beam to transform aportion of the pre-transformed material to a form a first porous layer,wherein the first porous layer is connected to the hard material and hasa horizontally non-overlapping portion with the hard material, whichfirst transformed material is formed anchorlessly within the enclosure,and operation (ii) direct the energy beam to transform the first porouslayer to form a first denser layer that is connected to the hardmaterial to form at least a second segment of the at least onethree-dimensional object that includes the first segment.

In some embodiments, the energy beam in operation (i) and in operation(ii) differ by a least one energy beam characteristic. In someembodiments, the energy beam in operation (i) and in operation (ii)differ by a least one energy beam characteristic comprising a velocity,a cross section, a power density, a fluence, a duty cycle, a dwell time,a focus, or a delay time. In some embodiments, the energy beam inoperation (i) is configured to emit radiation having a smaller crosssection as compared to its configuration in operation (ii). In someembodiments, the energy beam in operation (i) is configured to irradiateat a higher power density as compared to its configuration in operation(ii). In some embodiments, the energy beam in operation (i) isconfigured to irradiate at a shorter dwell time at a position ascompared to its configuration in operation (ii). In some embodiments,the energy beam in operation (i) is configured to continuously move,whereas energy beam in operation (ii) is configured to be stationary andmove interchangeably. In some embodiments, the energy beam in operation(i) is configured to be focused, whereas the energy beam in operation(ii) is configured to be de-focused. In some embodiments, the energybeam is a type-2 energy beam that comprises (i) a cross section that isat least 200 micrometers, or (ii) a power density of at most 8000 Wattsper millimeter square. In some embodiments, the energy beam is a type-1energy beam that comprises (i) a cross section that is smaller than 200micrometers, or (ii) a power density larger than 8000 Watts permillimeter square. In some embodiments, the at least one controller isfurther programmed to perform the following operations: operation (I)provide a layer of pre-transformed material adjacent to the first denserlayer, operation (II) direct the energy beam to transform a portion ofthe layer of pre-transformed material to form a second porous layer,wherein the second porous layer is connected to the first denser layer,and operation (III) direct the energy beam to densify at least a portionof the second porous layer to form a second dense layer portion as apart of the at least one three-dimensional object. In some embodiments,the energy beam in operation (I) and in operation (II) differ by atleast one energy beam characteristic. In some embodiments, the at leastone energy beam characteristic comprises a velocity, a cross section, apower density, a fluence, a duty cycle, a dwell time, a focus, a delaytime, a continuity of movement. In some embodiments, the energy beam inoperation (I) is configured to emit radiation having a smaller crosssection as compared to its configuration in operation (II). In someembodiments, the energy beam in operation (I) is configured to irradiateat a higher power density as compared to its configuration in operation(II). In some embodiments, the energy beam in operation (I) isconfigured to irradiate at a shorter dwell time at a position ascompared to its configuration in operation (II). In some embodiments,the energy beam in operation (I) is configured to continuously move,whereas energy beam in operation (II) is configured to be stationary andmove interchangeably. In some embodiments, the energy beam in operation(I) is configured to be focused, whereas the energy beam in operation(II) is configured to be de-focused. In some embodiments, the energybeam is a type-2 energy beam that comprises (I) a cross section that isat least 200 micrometers, or (II) a power density of at most 8000 Wattsper millimeter square. In some embodiments, the energy beam is a type-1energy beam that comprises (1) a cross section that is smaller than 200micrometers, or (II) a power density larger than 8000 Watts permillimeter square.

In another aspect, an apparatus for three-dimensional printing of atleast one three-dimensional object comprises at least one controllerthat is programmed to direct performance of the following operations:operation (a) provide a material bed that comprises a pre-transformedmaterial and a first hardened material that is a first segment of the atleast one three-dimensional object; operation (b) direct an energy beamto transform a portion of the pre-transformed material to a form aporous layer, wherein the porous layer is connected to the firsthardened material and has a horizontally non-overlapping portion withthe first hardened material, which first transformed material is formedanchorlessly within an enclosure, wherein the energy beam is operativelycoupled to the material bed; and operation (c) direct the energy beam totransform at least a portion of the porous layer to form a first denserlayer portion that is connected to the first hardened material to format least a second segment of the at least one three-dimensional objectthat includes the first segment.

In some embodiments, the at least one controller is a multiplicity ofcontrollers and wherein at least two of operation (a), operation (b),and operation (c) are directed by the same controller. In someembodiments, the at least one controller is a multiplicity ofcontrollers and wherein at least two of operation (a), operation (b),and operation (c) are directed by different controllers.

In another aspect, a computer software product for three-dimensionalprinting of at least one three-dimensional object, comprises anon-transitory computer-readable medium in which program instructionsare stored, which instructions, when read by a computer, cause thecomputer to perform operations comprising: operation (a) directing toprovide a material bed that comprises a pre-transformed material and afirst hardened material that is a first segment of the at least onethree-dimensional object; operation (b) directing an energy beam totransform a portion of the pre-transformed material to a form a porouslayer, wherein the porous layer is connected to the first hardenedmaterial and has a horizontally non-overlapping portion with the firsthardened material, which first transformed material is formedanchorlessly within an enclosure, wherein the energy beam is operativelycoupled to the material bed; and operation (c) directing the energy beamto transform at least a portion of the porous layer to form a firstdenser layer portion that is connected to the hardened material to format least a second segment of the at least one three-dimensional objectthat includes the first segment.

In another aspect, forming a three-dimensional object comprises: (a)providing a layer of pre-transformed material on an exposed surface of amaterial bed that comprises a hard portion that is a segment of thethree-dimensional object, which hard portion comprises an edge; and (b)forming a ledge of hardened material along the edge, which forming theledge comprises: (1) transforming the at least the portion of the layerof pre-transformed material to a transformed material at a positionusing an energy beam chiming a time period to form a tile, which firstposition is along a path-of-tiles, wherein during the time period theenergy beam is stationary or substantially stationary (e.g., such thatit at most undergoes pendulum and/or circular movement about theposition on the exposed surface); (2) translating the energy beam to asecond position along the path-of-tiles, which second position isdifferent from the first position, wherein the energy beam is translatedduring an intermission without transforming the pre-transformed materialalong the path-of-tiles; and (3) repeating (1) and (2) until reaching anend of the path-of-tiles that is parallel to or at the edge, wherein thetile overlaps the hard portion and extends beyond the edge towards thepre-transformed material of the material bed to form the ledge.

In some embodiments, transforming is by using an energy beam that has apower density of at most about 8000 Watts per millimeter squared (W/mm2)at the material bed. In some embodiments, the tile is a depositedtransformed material. In some embodiments, the edge is a first edge, andthe ledge forms a second edge. In some embodiments, the method furthercomprises repeating providing the layer of pre-transformed material onthe exposed surface of the material bed and transforming the at leastthe portion of the layer of pre-transformed material in (b) to elongatethe ledge. In some embodiments, the method further comprisestransforming at least a fraction of the ledge using a high aspect ratioenergy beam. In some embodiments, high aspect ratio energy beam forms amelt pool having a greater depth than width. In some embodiments, adepth of the melt pool is greater than a thickness of the tile. In someembodiments, the high aspect ratio energy beam transforms more than twolayers of tiles. In some embodiments, transforming at least the fractionof the ledge comprises re-melting at least the fraction of the ledge. Insome embodiments, transforming at least the fraction of the ledgereduces a porosity of the ledge. In some embodiments, repeating (1) and(2) results in forming a plurality of tiles. In some embodiments, afirst tile and a second tile of the plurality of tiles overlap with eachother. In some embodiments, the second tile is successive to the firsttile. In some embodiments, (b) comprises forming a first layer of tiles,wherein the method further comprises: forming a second layer of tiles.In some embodiments, centers of adjacent tiles of the plurality of tilesin the first layer are spaced apart by a first distance. In someembodiments, centers of adjacent tiles of the plurality of tiles in thesecond layer are spaced apart by a second distance. In some embodiments,the first distance is different than the second distance. In someembodiments, the first distance is the same as the second distance. Insome embodiments, the first and/or second distance ranges between about10 micrometers and about 500 micrometers. In some embodiments, (b)comprises forming a bottom skin of the three-dimensional object. In someembodiments, an exterior surface of the bottom skin has an area surfaceroughness (Sa) of at most about 20 micrometers. In some embodiments, thehard portion is formed by transforming at least a first portion ofpre-transformed material to a first transformed material that hardens ata first solidification rate. In some embodiments, forming the ledge ofhardened material in (b) is formed by transforming at least a secondportion of pre-transformed material to a second transformed materialthat hardens at a second solidification rate different than the firstsolidification rate. In some embodiments, an exterior surface of thebottom skin has an area surface roughness (Sa) of at most about 10micrometers. In some embodiments, the hard portion comprises a pluralityof layers that are stacked layerwise to form the hard portion, a layerof the plurality of layers defines a layering plane. In someembodiments, a stacking vector corresponds to a stacking direction ofthe plurality of layers. In some embodiments, stacking vector is normalto the layering plane. In some embodiments, a ledge vector is normal toa surface at a point on an exterior surface of the ledge and is in adirection of an interior of the ledge. In some embodiments, the ledgevector has a positive projection onto the stacking vector, wherein thestacking direction of the plurality of layers is indicative from (1) anydirectional melt pool that is included in the plurality of layers. (2) adirection opposite from any auxiliary supports or auxiliary supportmarks, (3) a direction of a surface comprising hatch decompositionmarking. (4) any asymmetric surface roughness indicative of printorientation, or (5) any directionality in grain orientation. In someembodiments, the ledge vector forms an angle with the stacking vectorthat is at most about forty-five degrees, and at least about zerodegrees. In some embodiments, the ledge vector forms an angle with thestacking vector that is at most about thirty degrees, and at least aboutzero degrees. In some embodiments, the ledge vector forms an angle withthe stacking vector that is at most about ten degrees, and at leastabout zero degrees.

In another aspect, printing a three-dimensional object comprises one ormore controllers that is programmed to: (a) direct a layer dispenser toprovide a layer of pre-transformed material on an exposed surface of amaterial bed comprising a hard portion that is a segment of thethree-dimensional object, which hard portion comprises an edge; and (b)direct forming a ledge of hardened material along the edge, which directforming the ledge comprises: (1) direct transforming the at least theportion of the layer of first pre-transformed material to a firsttransformed material at a first position by directing an energy beamduring a first time period to form a first tile, which first position isalong a path-of-tiles, wherein during the first time period, the energybeam is stationary or substantially stationary (e.g., such that it atmost undergoes pendulum and/or circular movement about the firstposition on the exposed surface); (2) direct translating the energy beamto a second position along the path-of-tiles, which second position isdifferent from the first position, wherein the energy beam is translatedduring an intermission without transforming the pre-transformed materialalong the path-of-tiles; and (3) direct repeating (1) and (2) untilreaching an end of the path-of-tiles, wherein the path-of-tiles isparallel to the edge or at the edge, wherein the first tile and thesecond tile overlap the hard portion and extend beyond the edge towardsthe pre-transformed material of the material bed to form the ledge.

In some embodiments, the hard portion comprises a plurality of layersthat defines a layering plane. In some embodiments, a vector normal toan exterior surface of the ledge that directs into the object thatintersects (i) the layering plane or (ii) a plane parallel to thelayering plane, forms an angle with respect to the layering plane. Insome embodiments, the angle is at least sixty degrees and at most ninetydegrees. In some embodiments, the vector is directed towards the ledge.In some embodiments, the one or more controllers controls at least onecharacteristic of the energy beam or of an energy source that generatesthe energy beam. In some embodiments, the one or more controllers atleast partially consider data from one or more sensors. In someembodiments, the data comprises temperature, optical and/orspectroscopic data. In some embodiments, the one or more controllers atleast partially consider a detection of electromagnetic radiation thatis emitted and/or reflected from an exposed surface of one or more meltpools formed during forming the ledge. In some embodiments, controllingconsiders a monitoring of a plastic yielding of a bottom skin formedduring forming the ledge. In some embodiments, the controlling considersa threshold value associated with (I) a temperature at the first and/orsecond position. (II) a power density of the energy beam at the exposed,surface of the material bed, (III) a power of an energy sourcegenerating the energy beam, or (IV) any combination of (I), (II) or(III). In some embodiments, the one or more controllers directs feedbackor closed loop control. In some embodiments, the one or more controllersdirects feed-forward or open loop control. In some embodiments, the oneor more controllers directs real time control during (a), (b), (c)and/or (d). In some embodiments, the one or more controllers control atleast one characteristic of the energy beam during formation of theledge. In some embodiments, the at least one characteristic comprisesirradiation time, intermission time, power density, speed,cross-section, focus, or power density profile over time, in someembodiments, the one or more controllers control a temperature of anexposed surface of a melt pool formed during formation of the ledge bycontrolling one or more characteristics of the energy beam, in someembodiments, the at least one characteristic comprises irradiation time,intermission time, power density, speed, cross-section, focus, or powerdensity profile over time. In some embodiments, the one or morecontrollers controls a temperature of an exposed surface of a melt poolformed during formation of the ledge. In some embodiments, controllingthe temperature comprises causing an energy source to alter a powerdensity of the energy beam during at least a portion of forming theledge. In some embodiments, controlling the temperature comprisescausing an energy source to alter a scan speed of the energy beam duringat least a portion of forming the ledge in (c). In some embodiments, theone or more controllers control a depth of a melt pool formed duringforming the first and/or second tile formed daring formation of theledge by controlling one or more characteristics of the energy beam. Insome embodiments, the one or more controllers controls a depth of one ormore melt pools formed daring forming the ledge in (c). In someembodiments, the one or more controllers is programmed to directadjusting one or more characteristics of the energy beam before, duringor after forming the ledge in (c). In some embodiments, the one or morecharacteristics of the energy beam is adjusted to accomplish asolidification rate during forming the ledge in (c) that is differentthan a solidification rate used to for the hard portion. In someembodiments, the one or more controllers is programmed to directperformance of an alternate method to (b), namely: direct using ahatching energy beam during forming the ledge in (c). In someembodiments, hatching comprises continuous irradiation of a targetsurface during movement of the first and/or second energy beam along apath. In some embodiments, the hard portion comprises a plurality oflayers that are stacked layerwise to form the hard portion, a layer ofthe plurality of layers defines a layering plane. In some embodiments, astacking vector corresponds to a stacking direction of the plurality oflayers. In some embodiments, stacking vector is normal to the layeringplane. In some embodiments, a ledge vector is normal to a surface at apoint on an exterior surface of the ledge and is in a direction of aninterior of the ledge. In some embodiments, the ledge vector has apositive projection onto the stacking vector, wherein the stackingdirection of the plurality of layers is indicative from (1) anydirectional melt pool that is included in the plurality of layers, (2) adirection opposite from any auxiliary supports or auxiliary supportmarks. (3) a direction of a surface comprising hatch decompositionmarking, (4) any asymmetric surface roughness indicative of printorientation, or (5) any directionality in grain orientation. In someembodiments, the ledge vector forms an angle with the stacking vectorthat is at most about forty-five degrees, and at least about zerodegrees. In some embodiments, the ledge vector forms an angle with thestacking vector that is at most about thirty degrees, and at least aboutzero degrees.

In another aspect, a method of forming a three-dimensional objectcomprises: (a) providing a material bed comprising a pre-transformedmaterial and a hard portion that is a segment of the three-dimensionalobject, wherein the material bed is disposed on a platform; (b) using atype-2 energy beam to transform at least a portion of thepre-transformed material to a form a first transformed material portionthat (i) connects to the hard portion and (ii) comprises a horizontallynon-overlapping section with the hard portion, wherein the type-2 energybeam has a power density of at most 8000 Watts per millimeter squared(W/mm²), (c) providing a layer of pre-transformed material adjacent toan exposed surface of the material bed; and using the type-2 energy beamto transform at least a portion of the layer of pre-transformed materialto a form a second transformed material portion that (i) connects to thefirst transformed material portion and (ii) comprises a horizontallynon-overlapping section with the first transformed material portion,wherein the first transformed material portion and the secondtransformed material portion form (I) an overhang or (II) a cavityceiling, that form an angle of at most thirty (30) degrees with theexposed surface of the material bed and/or with the platform.

In some embodiments, the type-2 energy beam has a power density of atmost about 8000 Watts per millimeter square. In some embodiments, thehard portion is suspended anchorlessly in the material bed during theprinting. In some embodiments, the hard portion is anchored to theplatform during the printing. In some embodiments, anchored is directlyanchored to a base above which the material bed is disposed. In someembodiments, anchored comprises anchored through one or more auxiliarysupports. In some embodiments, the horizontally non-overlapping sectionforms at least a segment of an overhang or a cavity ceiling. In someembodiments, the overhang or cavity ceiling form an angle with theexposed surface of the material bed and/or with the platform above whichthe material bed is disposed, wherein the angle is from zero to thirtydegrees. In some embodiments, the angle is from ten to thirty degrees.In some embodiments, the horizontally non-overlapping section comprisesa bottom skin surface that faces the platform above which the materialbed is disposed. In some, embodiments, the bottom skin surface has anarithmetic average of a roughness profile of at most 200 micrometers. Insome embodiments, the bottom skin surface has an arithmetic average of aroughness profile of at most 50 micrometers. In some embodiments, themethod further comprises after operation (c), using an energy beam totransform a portion of the pre-transformed material to form a porouslayer portion disposed at least in part above the first transformedmaterial portion to form a part of the three-dimensional object, whereinthe energy beam is the same or different from the type-2 energy beam. Insome embodiments, the method further comprises using the energy beam todensity the porous layer portion to form a denser portion as part of thethree-dimensional object. In some embodiments, the denser portion, theporous layer portion, or the denser portion and the porous layerportion, connect to the first transformed material portion. In someembodiments, the first transformed material portion that is connected tothe porous layer portion and/or the denser portion forms a thickenedoverhang structure. In some embodiments, adjacent comprises above. Insome embodiments, adjacent comprises overlapping. In some embodiments,adjacent comprises bordering.

In another aspect, a system for printing at least one three-dimensionalobject comprises: an enclosure that is configured to accommodate amaterial bed that comprises a pre-transformed material and a hardportion that is a first segment of the at least one three-dimensionalobject, wherein the material bed is disposed on a platform, an energysource that is configured to generate a type-2 energy beam (e.g., asdisclosed herein) that transforms a portion of the pre-transformedmaterial to form a second segment of the at least one three-dimensionalobject, wherein the type-2 energy beam has a power density of at most8000 Watts per millimeter squared (W/mm²), wherein the type-2 energybeam is operatively coupled to the enclosure; and at least onecontroller that is operatively coupled to the type-2 energy beam, whichthe at least one controller is programmed to perform the followingoperations: operation (i) direct the type-2 energy beam to transform atleast a portion of the pre-transformed material to a form a firsttransformed material portion that connects to the hard portion andcomprises a horizontally non-overlapping section with the hard portion,operation (ii) direct providing a layer of pre-transformed materialadjacent to an exposed surface of the material bed, and operation (iii)direct the type-2 energy beam to transform at least a portion of thelayer of pre-transformed material to a form a second transformedmaterial portion that connects to the first transformed material portionand comprises a horizontally non-overlapping section with the firsttransformed material portion, wherein the first transformed materialportion and the second transformed material portion generate the secondsegment that comprises (I) an overhang or (II) a cavity ceiling, whichsecond segment forms an angle of at most thirty (30) degrees with theexposed surface of the material bed and/or with the platform,

In some embodiments, the type-2 energy beam translates in a step andmove mode, wherein in the step and move mode (e.g., tiling methodologyas disclosed herein), the type-2 energy beam is stationary orsubstantially stationary. In some embodiments, the type-2 energy beam isa first type-2 energy beam, wherein the at least one controller isprogrammed to perform the following operations after (iii), operation(iv) direct a second type-2 energy beam to transform a portion of thepre-transformed material to form a porous layer portion disposed atleast in part above the first transformed material portion as part ofthe at least one three-dimensional object, wherein the second type-2energy beam is the same or different from the first type-2 energy beam.In some embodiments, the at least one controller is programmed tofurther perform the following operation: direct the first or secondtype-2 energy beam to densify the porous layer portion to form a denserportion as part of the at least one three-dimensional object. In someembodiments, the denser portion, the porous layer, or the denser portionand the porous layer portion, connect to the first transformed materialportion. In some embodiments, the first transformed material portionthat is connected to the porous layer and/or denser portion forms athickened overhang structure. In some embodiments, the at least onecontroller is a multiplicity of controllers and wherein at least two ofoperation (i), operation (ii), and operation (iii) are directed by thesame controller. In some embodiments, the at least one controller is amultiplicity of controllers and wherein at least two of operation (i),operation (ii), and operation (iii) are directed by differentcontrollers.

In another aspect, an apparatus for three-dimensional printing of atleast one three-dimensional object comprises at least one controllerthat is programmed to perform the following operations: operation (a)direct providing a material bed comprising a pre-transformed materialand a hard portion that is a first segment of the at least onethree-dimensional object, wherein the material bed is disposed on aplatform, operation (b) direct a type-2 energy beam to transform atleast a portion of the pre-transformed material to a form a firsttransformed material portion that (i) connects to the hard portion and(ii) comprises a horizontally non-overlapping section with the hardportion, (e.g., wherein the type-2 energy beam has a power density of atmost 8000 Watts per millimeter squared (W/mm²)) wherein the type-2energy beam is operatively coupled to the material bed: operation (c)provide a layer of pre-transformed material adjacent to an exposedsurface of the material bed: and operation (d) direct the type-2 energybeam to transform at least a portion of the layer of pre-transformedmaterial to a form a second transformed material portion that (i)connects to the first transformed material portion and (ii) comprises ahorizontally non-overlapping section with the first transformed materialportion, wherein the first transformed material portion and the secondtransformed material portion form (I) an overhang or (II) a cavityceiling, that forms an angle of at most thirty (30) degrees with theexposed surface of the material bed and/or with the platform.

In some embodiments, the at least one controller is a multiplicity ofcontrollers and wherein at least two of operation (a), operation (b),operation (c), and operation (d) are directed by the same controller. Insome embodiments, the at least one controller is a multiplicity ofcontrollers and wherein at least two of operation (a), operation (b),operation (c), and operation (d) are directed by different controllers.

In another aspect, a computer software product for three-dimensionalprinting of at least one three-dimensional object, comprises anon-transitory computer-readable medium in which program instructionsare stored, which instructions, when read by a computer, cause thecomputer to perform operations comprising: operation (a) providing amaterial bed comprising a pre-transformed material and a hard portionthat is a first segment of the at least one three-dimensional object,wherein the material bed is disposed on a platform; operation (b)directing a type-2 energy beam to transform at least a portion of thepre-transformed material to a form a first transformed material portionthat (i) connects to the hard portion and (ii) comprises a horizontallynon-overlapping section with the hard portion, (e.g., wherein the type-2energy beam has a power density of at most 8000 Watts per millimetersquared (W/mm₂)) wherein the type-2 energy beam is operatively coupledto the material bed; operation (c) providing a layer of pre-transformedmaterial adjacent to an exposed surface of the material bed; andoperation (d) directing the type-2 energy beam to transform at least aportion of the layer of pre-transformed material to a form a secondtransformed material portion that (i) connects to the first transformedmaterial portion and (ii) comprises a horizontally non-overlappingsection with the first transformed material portion, wherein the firsttransformed material portion and the second transformed material portionform (I) an overhang or (II) a cavity ceiling, that form an angle of atmost thirty (30) degrees with the exposed surface of the material bedand/or with the platform.

In another aspect, a three-dimensional object comprises: a plurality oflayers of hard material stacked and bonded together to form a shape ofthe three-dimensional object, wherein a boundary between two of theplurality of layers defines a layering plane, which plurality of layerscomprises: a first section comprising a first microstructure associatedwith being formed at a first solidification rate; and a second sectioncomprising: (i) a second microstructure associated with being formed ata second solidification rate that is different from the firstsolidification rate, and (ii) an exterior surface corresponding to atleast a fraction of an exterior surface of the three-dimensional object,wherein a vector normal to a point on the exterior surface of the secondsection that intersects (1) the layering plane or (2) a plane parallelto the layering plane, defines a non-perpendicular angle with respect tothe layering plane.

In some embodiments, the plurality of layers defines a stacking vectorindicative (e.g., characteristic, or typical) of a direction oflayerwise printing of the three-dimensional object. In some embodiments,the vector normal to a surface at the point on the exterior surface ofthe second section that intersects the stacking vector defines anon-parallel angle with respect to the stacking vector. In someembodiments, the first section is characterized as comprising the firstmicrostructure and wherein the second section is characterized ascomprising the second microstructure. In some embodiments, the layeringplane is perpendicular to the stacking vector. In some embodiments, asurface of the three-dimensional object includes a support mark regionindicative of one or more auxiliary supports used to support thethree-dimensional object during its printing. In some embodiments, thesupport mark region is characterized as having (I) an alteration on asurface of the support mark region, (II) a material variation within avolume of the support mark region, or (III) both (I) and (II). In someembodiments, the first and second sections are coupled with each other.In some embodiments, the first and second sections are (e.g., chemically(e.g., metallically)) bonded with each other. In some embodiments, thesecond solidification rate is slower than the first solidification rate.In some embodiments, the second solidification rate is faster than thefirst solidification rate. In some embodiments, the first solidificationrate is associated with a first cooling rate. In some embodiments, thesecond solidification rate is associated with a second cooling ratedifferent than the first cooling rate. In some embodiments, the firstmicrostructure and the second microstructure each comprise a melt pool,or a grain structure. In some embodiments, the grain structure comprisesa cell or a dendrite. In some embodiments, the grain structure comprisesa crystal. In some embodiments, the grain structure comprises a metalmicrostructure. In some embodiments, the second section corresponds to askin of the three-dimensional object. In some embodiments, the skin hasa thickness ranging from about 20 micrometers to about 1000 micrometers.In some embodiments, the skin has a thickness ranging from about 20micrometers to about 400 micrometers. In some embodiments, the secondmicrostructure comprises at least one melt pool. In some embodiments,the second section defines an alignment line that runs through a centralportion of the at least one melt pool and/or along the exterior surfaceof the second section. In some embodiments, the second microstructurecomprises grain structures that are aligned with respect to thealignment line. In some embodiments, the second section is characterizedby (a) a melt pool that defines an alignment line that runs through acentral portion of the melt pool, and (b) a plurality of grainstructures that converge along the alignment line. In some embodiments,grains of the plurality of grain structures are aligned towards (e.g.,converge or lean towards) at a non-zero angle relative to the alignmentline. In some embodiments, the first section comprises a first set ofgrains. In some embodiments, the second section comprises a second setof grains. In some embodiments, grains of the second set have (e.g., onaverage) a different property than the first set comprising: afundamental length scale, a chemical makeup, a crystal structure, acoherence length, a morphology, a metallurgical microstructure, or analignment. In some embodiments, the fundamental length scale comprises alength or a width. In some embodiments, the first section comprises afirst set of dendrites. In some embodiments, the second sectioncomprises a second set of dendrites. In some embodiments, dendrites ofthe second set are (e.g., on average) thicker than dendrites of thefirst set. In some embodiments, grains of the second set have afundamental length scale that is (e.g., on average) about 1.5 timesgreater than grains of the first set. In some embodiments, grains of thesecond set have a greater coherence length than grains of the first set.In some embodiments, the three-dimensional object comprises a skin. Insome embodiments, an exterior surface of the skin has a plurality ofcrescent-shaped ridges corresponding to overlapping tiles,

In another aspect, a three-dimensional object comprises: a plurality oflayers of hardened material stacked and bonded together to form a shapeof the three-dimensional object, wherein a boundary between two of theplurality of layers defines a layering plane, which plurality of layerscomprises an overhang portion having an exterior surface correspondingto at least a fraction of an exterior surface of the three-dimensionalobject, wherein a vector normal to a surface at a point on the exteriorsurface of the overhang portion that intersects (i) the layering planeor (ii) a plane parallel to the layering plane, defines an angle withrespect to the layering plane, wherein the overhang portion comprises: afirst section of the exterior surface of the overhang portioncharacterized as having a first surface roughness; and a second sectionof the exterior surface of the overhang portion characterized as havinga second surface roughness.

In some embodiments, the first and second sections are bonded with eachother. In some embodiments, the first section is disposed at one side ofthe overhang. In some embodiments, the second section is disposed at anopposing side of the overhang. In some, embodiments, the exteriorsurface of the overhang comprises the first section and the secondsection that are disposed at a side of the overhang. In someembodiments, angle is from about sixty degrees to about ninety degrees.In some embodiments, each of the plurality of layers comprises a meltpool, that has a directionality corresponding to its deposition. In someembodiments, a stacking vector corresponding to a layerwise depositionof the plurality of layers is perpendicular to the layering plane and inthe direction of the layerwise deposition as indicative by thedirectionality of the melt pool. In some embodiments, a positive acuteangle between a vector normal to a surface at a point of an exposedsurface of the overhang that points towards the overhang, and thestacking vector, is in a range of from zero to at most thirty degrees.In some embodiments, a positive acute angle between the vector normal toa surface at the point of the exposed surface of the overhang thatpoints towards the overhang, and the stacking vector, is in a range offrom zero to at most fifteen degrees. In some embodiments, the firstsurface roughness and the second surface roughness have an arithmeticaverage of a roughness profile (Ra) value of at most 20 micrometers. Insome embodiments, the first surface roughness and/or the second surfaceroughness have an arithmetic average of a roughness profile (Ra) valueof at most 10 micrometers. In some embodiments, the first surfaceroughness and the second surface roughness are detectably different. Insome embodiments, the three-dimensional object has no detectable markthat it underwent further processing after its printing. In someembodiments, the first roughness is at least 2 times rougher than thesecond roughness. In some embodiments, the first section comprises afirst core portion and a first skin portion. In some embodiments, thefirst and second sections are (e.g., chemically (e.g., metallically))bonded with each other. In some embodiments, the first section ischaracterized as being formed at a first solidification rate. In someembodiments, the second section is characterized as being formed at asecond solidification rate that is slower than the first solidificationrate. In some embodiments, the first section is characterized as beingformed at a first solidification rate. In some embodiments, the secondsection is characterized as being formed at a second solidification ratethat is faster than the first solidification rate. In some embodiments,the first section is characterized as being formed at a firstsolidification rate that is associated with a first cooling rate. Insome embodiments, the second section is characterized as being formed ata second solidification rate that is associated with a second coolingrate (e.g., different than the first cooling rate). In some embodiments,the first section comprises first microstructure. In some embodiments,the second section comprises a second microstructure. In someembodiments, the first and second microstructure comprise melt pools orgrains. In some embodiments, the grains comprise a cell or a dendrite.In some embodiments, the grains comprise a crystal. In some embodiments,the grains comprise a metallurgical microstructure. In some embodiments,the first section includes a skin portion and a core portion. In someembodiments, the skin portion is characterized by an alignment line thatruns through a central portion of a melt pool of the skin portion and/oralong the exterior surface of the second section. In some embodiments,the second microstructure comprises grain structures that are alignedwith respect to the alignment line. In some embodiments, the firstsection includes a skin portion and a core portion, wherein the skinportion is characterized by (a) a melt pool that defines an alignmentline that runs through a central portion of the melt pool, and (b) aplurality of grain structures of the melt pool that converge along thealignment line. In some embodiments, the grain structures converge at anon-zero angle. In some embodiments, the first section comprises a firstset of grains. In some embodiments, the second section comprises asecond set of grains. In some embodiments, grains of the second set havea different property than the first set. In some embodiments, thedifferent property comprises: a fundamental length scale, a chemicalmakeup, a crystal structure, a coherence length, a morphology, ametallurgical microstructure, or an alignment. In some embodiments, thefundamental length scale comprises thickness or length. In someembodiments, the grains of the second set have a greater coherencelength than the grains of the first set. In some embodiments, the grainof the second set are (e.g., on average) about 1.5 times thicker thanthe grain of the first set. In some embodiments, the second section ischaracterized as having a high aspect ratio melt pool. In someembodiments, the high aspect ratio melt pool is characterized as havinga greater depth than width. In some embodiments, the layering plane isperpendicular to a stacking vector of the stacked layer. In someembodiments, the three-dimensional object comprises a skin. In someembodiments, an exterior surface of the skin has a plurality ofcrescent-shaped ridges corresponding to overlapping tiles. In someembodiments, the first section is disposed at one side of the overhangportion. In some embodiments, the second section is disposed at anopposing side of the overhang portion. In some embodiments, the exteriorsurface of the overhang portion comprises the first section and thesecond section that are disposed at a side of the overhang portion. Insome embodiments, the first surface roughness is at least 2 timesgreater than the second surface roughness.

In another aspect, a three-dimensional object comprises: a plurality oflayers of hard material stacked layerwise and bonded together to form ashape of the three-dimensional object, wherein a layer of the pluralityof layers defines a layering plane, which plurality of layers comprises:a first section comprising a first microstructure associated with beingformed at a first solidification rate; and a second section is at leasta portion of an overhang comprising: (i) second microstructureassociated with being formed at a second solidification rate that isdifferent from the first solidification rate, and (ii) an exteriorsurface corresponding to at least a fraction of an exterior surface ofthe three-dimensional object, wherein an overhang vector at a point onthe exterior surface of the second section is normal to a surface at thepoint in a direction towards an interior of the overhang, wherein astacking vector corresponds to a stacking direction of the plurality oflayers, which stacking vector is normal to the layering plane, whereinthe overhang vector has a positive projection onto the stacking vector,wherein the stacking direction of the plurality of layers is indicativefrom (1) any directional melt pool that is included in the plurality oflayers, (2) a direction opposite from any auxiliary supports orauxiliary support marks, (3) a direction of a surface comprising hatchdecomposition marking, (4) any asymmetric surface roughness, or (5) anydirectionality in grain orientation, indicative of print orientation.

In some embodiments, the first section is characterized as comprisingthe first microstructure and wherein the second section is characterizedas comprising the second microstructure. In some embodiments, the firstand second sections are coupled with each other. In some embodiments,the second solidification rate is slower than the first solidificationrate. In some embodiments, the first microstructure and secondmicrostructure each comprise a melt pool, or a grain structures. In someembodiments, the grain structure comprises a crystal. In someembodiments, the second section corresponds to a skin of thethree-dimensional object. In some embodiments, the skin has a thicknessranging from about 20 micrometers to about 1000 micrometers. In someembodiments, the skin has corresponding to a fundamental length scale ofa melt pool. In some embodiments, the second section is characterized byan alignment line that runs through a central portion of the melt pooland/or along the exterior surface of the second section. In someembodiments, the second microstructure comprises grain structures thatare aligned with respect to the alignment line. In some embodiments, thegrain structures are aligned at a non-zero angle relative to thealignment line. In some embodiments, the first section comprises a firstset of grains. In some embodiments, the second section comprises asecond set of grains. In some embodiments, grains of the second set haveon average a different property than the first set comprising: afundamental length scale, a chemical makeup, a crystal structure, acoherence length, a morphology, a metallurgical microstructure, or analignment. In some embodiments, the grains of the second set have afundamental length scale that is on average about 1.5 times thicker thanthe grains of the first set. In some embodiments, the grains of thesecond set have a greater coherence length, fundamental length scale,and/or alignment. In some embodiments, the overhang vector forms anangle with the stacking vector that is at most about forty-five degrees,and at least about zero degrees. In some embodiments, the overhangvector forms an angle with the stacking vector that is at most aboutthirty degrees, and at least about zero degrees. In some embodiments,the overhang vector forms an angle with the stacking vector that is atmost about ten degrees, and at least about zero degrees. In someembodiments, the first and second sections are bonded with each other.In some embodiments, the first section has a first surface roughness andthe second surface has a second surface roughness. In some embodiments,the first surface roughness and the second surface roughness have anarithmetic average of a roughness profile (Ra) value of at most about 20micrometers. In some embodiments, the first surface roughness and/or thesecond surface roughness have an arithmetic average of a roughnessprofile (Ra) value of at most 10 micrometers. In some embodiments, thefirst section has a first surface roughness and the second surface has asecond surface roughness that is delectably different from the firstsurface roughness. In some embodiments, the first roughness is at least2 times rougher than the second roughness. In some embodiments, theoverhang is a three-dimensional plane. In some embodiments, the overhangis a ledge. In some embodiments, the melt pool comprises a narrow bottomportion and a broader top portion. In some embodiments, the auxiliarysupport marks comprise a point of discontinuity of layer structure akina foreign object. In some embodiments, the hatch decomposition markingrelates to a hatch strategy that divides a top surface into segments. Insome embodiments, two directly adjacent segments differ by at least in ahatching direction from one another. In some embodiments, the asymmetricsurface roughness indicative of print orientation is caused by a printprocess in which the bottom surface has a different roughness than thetop surface.

In another aspect, a three-dimensional object comprises: a plurality oflayers of hardened material that are metallically bonded together,wherein a layer of the plurality of layers has a layering plane, whereinthe plurality of layers comprises: a core portion comprising a firstplurality of layers, which core portion comprises a first microstructureassociated with being formed at a first solidification rate, and a skinportion that is metallically bonded with the core portion and comprisinga second plurality of layers, wherein: (i) an exterior surface of theskin portion corresponds to at least a fraction of an exterior surfaceof the three-dimensional object, and (ii) the skin portion ischaracterized as having a second microstructure associated with beingformed at a second solidification rate that is different than the firstsolidification rate, wherein a stacking vector is in a direction inwhich the plurality of layers were stacked together during formation ofthe three-dimensional object, wherein the skin portion is at least aportion of an overhang, wherein an overhang vector is normal to asurface at a point on the exterior surface of the skin portion and is ina direction of an inferior of the overhang, wherein the overhang vectorhas a positive projection onto the stacking vector, wherein a stackingdirection of the plurality of layers is indicative from (1) anydirectional melt pool that is included in the plurality of layers. (2) adirection opposite from any auxiliary supports or auxiliary supportmarks, (3) a direction of a surface comprising hatch decompositionmarking, (4) any asymmetric surface roughness indicative of printorientation, or (5) any directionality in an orientation of grains ofthe three-dimensional object.

In some embodiments, the exterior surface of the skin portion comprisesa plurality of scales corresponding to a plurality of overlapping tiles.In some embodiments, the three-dimensional object comprises an elementalmetal, metal alloy, an allotrope of elemental carbon, a polymer, or aresin. In some embodiments, the first plurality of layers is alignedwith the second plurality of layers. In some embodiments, a second layerof the second plurality of layers is an extension of a correspondingfirst layer of the first plurality of layers. In some embodiments, thefirst solidification rate and the second solidification rate areassociated with a first cooling rates and a second cooling rate ofmolten material. In some embodiments, the first solidification rate isfaster than the second solidification rate. In some embodiments, thefirst solidification rate is slower than the second solidification rate.In some embodiments, the first microstructure comprises a first meltpool and/or a first grain. In some embodiments, the secondmicrostructure comprise a second melt pool and/or a second grain. Insome embodiments, the first grain comprises a first constituent and thesecond grain comprise a second constituent. In some embodiments, thefirst constituent differs from the second constituent in at least oneaspect comprising: fundamental length scale, chemical makeup, crystalstructure, metallurgical microstructure, or spatial placement in a meltpool. In some embodiments, the first constituent comprises a firstcrystal or a first metallurgical microstructure. In some embodiments,the second constituent comprises a second crystal or a secondmetallurgical microstructure. In some embodiments, the metallurgicalmicrostructure comprises a dendrite or a cell. In some embodiments, theskin portion has a thickness of a melt pool in a layer of the skinportion In some embodiments, the skin portion has a thickness equal to afundamental length scale of a melt pool. In some embodiments, the skinportion has a thickness ranging from about 20 micrometers to about 1000micrometers. In some embodiments, an alignment line runs parallel to anexposed surface of the skin portion, on the skin portion, or through acentral portion of a melt pool of the skin portion, and a plurality ofgrain structures of the skin portion are aligned towards the alignmentline or with respect to the alignment line. In some embodiments, thegrains converge in a V-shape towards the alignment line. In someembodiments, a top of the V-shape is pointed in accordance with thestacking vector. In some embodiments, the grain structures lean towardsthe alignment line and form a non-zero angle with respect to thelayering plane. In some embodiments, the skin portion comprisesdendrites that are oriented substantially parallel to the alignmentline. In some embodiments, substantially parallel comprises at an angleof at most about twenty degrees with respect to the alignment line. Insome embodiments, the skin portion comprises (i) a melt pool thatdefines an alignment line that runs through a central portion of themelt pool and (ii) a plurality of grain structures that converge alongthe alignment line. In some embodiments, the grain structures in themelt pool converge at a non-zero angle. In some embodiments, the coreportion comprises a first set of grains. In some embodiments, the skinportion comprises a second set of grains. In some embodiments, grains ofthe second set have on average a fundamental length scale that is largerthan grains of the first set. In some embodiments, the fundamentallength scale comprises a width or a length. In some embodiments, grainsof the second set are on average about 1.5 times thicker and/or longerthan grains of the first set. In some embodiments, the skin portion ischaracterized by a plurality of tiles. In some embodiments, centers oftwo successive tiles are substantially uniformly spaced apart from oneanother. In some embodiments, at least two adjacent tiles overlap witheach other. In some embodiments, the skin portion corresponds to abottom skin of an overhang structure of the three-dimensional object. Insome embodiments, a vector from a surface at a point on the exteriorsurface of the bottom skin intersects (a) the layering plane or (b) aplane parallel to the layering plane, forms an angle with respect to thelayering plane or with a line parallel to the layering plane. In someembodiments, the angle is at least about sixty degrees and at most aboutninety degrees. In some embodiments, the vector is directed into theoverhang structure. In some embodiments, the exterior surface has ameasured area surface roughness (Sa) of at most about 20 micrometers. Insome embodiments, the exterior surface has a measured area surfaceroughness (Sa) of at most about 5 micrometers. In some embodiments, thecore portion has substantially the same chemical composition as the skinportion. In some embodiments, the exterior surface of the skin portionhas a plurality of crescent-shaped ridges corresponding to overlappingtiles. In some embodiments, the overhang vector forms an angle with thestacking vector that is at most about forty-five degrees, and at leastabout zero degrees. In some embodiments, the overhang vector forms anangle with the stacking vector that is at most about thirty degrees, andat least about zero degrees. In some embodiments, the overhang vectorforms an angle with the stacking vector that is at most about tendegrees, and at least about zero degrees.

In another aspect, a method of printing a three-dimensional objectcomprises: (a) printing a target surface using a three-dimensionalprinting methodology in an enclosure; using an energy beam to irradiatein the enclosure a portion of the target surface comprising a materialto a form a well comprising first material portion that is in a moltenstate and a second material portion that is ejected to form a hole ofthe well, which energy beam irradiates using a first power densityprofile; and (b) irradiating the well with the energy beam in theenclosure using a second power density profile to close the hole andform a first melt pool that has a high aspect ratio as part of thethree-dimensional object.

In some embodiments, the first melt pool comprises a percentage of poresof at most ten (volume of pore per volume of melt pool). In someembodiments, the first melt pool comprises a percentage of pores of atmost five (volume of pore per volume of melt pool). In some embodiments,the first melt pool comprises a percentage of pores of at most two(volume of pore per volume of melt pool). In some embodiments, theenergy beam is a type-2 energy beam. In some embodiments, the type-2energy beam progresses along a trajectory in a step and move mode,wherein daring the step, the type-2 energy beam is stationary orsubstantially stationary. In some embodiments, the type-2 energy beamhas a cross section of at least about 200 micrometers. In someembodiments, the type-2 energy beam has a power density of at most about8000 Watts per millimeter square. In some embodiments, the energy beamis a type-1 energy beam. In some embodiments, the type-1 energy beam istranslating along a trajectory. In some embodiments, the type-1 energybeam has a cross section that is below about 200 micrometers. In someembodiments, the type-1 energy beam has a power density above about80000 Watts per millimeter square. In some embodiments, the methodfurther comprises translating while irradiating the well with the energybeam from a first position located in the well, to a second position onthe target surface that is adjacent to the well to subsequently form alaterally elongated melt pool. In some embodiments, translating theenergy beam comprises translating in a lateral direction. In someembodiments, comprises expanding the first material portion in themolten state in the lateral direction. In some embodiments, the targetsurface is an exposed surface of a material bed. In some embodiments,the target surface is an exposed surface of at least a section of thethree-dimensional object. In some embodiments, the target surface is anexposed surface of a porous layer. In some embodiments, the targetsurface is an exposed surface of a densified porous layer. In someembodiments, the high aspect ratio comprises a depth of the first meltpool that is larger than an average radius of an exposed surface of thefirst melt pool. In some embodiments, a maximum power density of thesecond power density profile is lower than a maximum power density ofthe first power density profile. In some embodiments, ejected comprisesvaporized. In some embodiments, the second material portion that isejected comprises plasma, molten spits, or evaporated material. In someembodiments, the three-dimensional printing methodology compriseslayerwise material deposition. In some embodiments, the well spans oneor more layers of the three-dimensional object. In some embodiments, thewell spans a plurality of layers of the three-dimensional object. Insome embodiments, the target surface comprises a horizontally narrowportion of the three-dimensional object. In some embodiments, the targetsurface comprises an overhang tip. In some embodiments, the methodfurther comprises :repeating operations (b) to (c) to form a second meltpool adjacent to the first melt pool. In some embodiments, the secondmelt pool is identical or substantially identical to the first meltpool. In some embodiments, the second melt pool is different than thefirst melt pool by at least one fundamental length scale,

In another aspect, a system for printing at least one three-dimensionalobject comprises: an enclosure that is configured to accommodate atarget surface that comprises a pre-transformed material; an energysource that is configured to generate an energy beam that energy beam toirradiate a portion of the target surface to form a part of the at leastone three-dimensional object, wherein the energy beam is operativelycoupled to the enclosure; and at least one controller that isoperatively coupled to the energy beam, which at least one controller iscollectively or separately programmed to perform the followingoperations: operation (i): direct the energy beam to irradiate in theenclosure a portion of the target surface comprising a material to aform a well comprising a first material portion that is molten and asecond material portion that is ejected to form a hole of the well,which energy beam irradiates at a first power density profile, andoperation (ii) direct the energy beam to irradiate the well in theenclosure at a second power density profile to close the hole and form afirst melt pool that has a high aspect ratio as part of the at least onethree-dimensional object.

In another aspect, an apparatus for three-dimensional printing of atleast one three-dimensional object comprises at least one controllerthat is programmed to collectively or separately perform the followingoperations: operation (a) direct printing a target surface using athree-dimensional printing methodology in an enclosure; operation (b)direct an energy beam to irradiate in the enclosure a portion of thetarget surface comprising a material to a form a well comprising firstmaterial portion that is molten and a second material portion that isejected to form a hole of the well, which energy beam irradiates at afirst power density profile, wherein the energy beam is operativelycoupled to the enclosure; and operation (c) direct the energy beam toirradiate the well with the energy beam in the enclosure at a secondpower density profile to close the hole and form a first melt pool thathas a high aspect ratio as part of the at least one three-dimensionalobject.

In another aspect, a computer software product for three-dimensionalprinting of at least one three-dimensional object, comprises anon-transitory computer-readable medium in Which program instructionsare stored, which instructions, when read by a computer, cause thecomputer to perform operations comprising: operation (a) directingprinting a target surface using a three-dimensional printing methodologyin an enclosure; operation (b) directing an energy beam to irradiate inthe enclosure a portion of the target surface comprising a material to aform a well comprising first material portion that is molten and asecond material portion that is ejected to form a hole of the well,which energy beam irradiates at a first power density profile, whereinthe energy beam is operatively coupled to the target surface; andoperation (c) directing the energy beam to irradiate the well with theenergy beam in the enclosure at a second power density profile to closethe hole and form a first melt pool that has a high aspect ratio as partof the at least one three-dimensional object.

In another aspect, a method of printing a three-dimensional objectcomprises: (a) providing a material bed comprising a pre-transformedmaterial; and (b) using an energy beam to transform a first portion ofthe pre-transformed material to a form a layer of transformed materialas a part of a sub-structure of the three-dimensional object, whichlayer transformed material comprises a plurality of melt pools havingidentical or substantially identical cross-sectional sizes.

In some embodiments, substantially identical comprise within fifteenpercent of their fundamental length scale. In some embodiments,substantially identical comprise within ten percent of their fundamentallength scale. In some embodiments, substantially identical comprisewithin five percent of their fundamental length scale. In someembodiments, wherein a fundamental length scale of the melt poolscomprises their respective (i) depth or (ii) radius of their exposedsurfaces. In some embodiments, the method further comprises controllingat least one characteristic of the energy beam or of an energy sourcethat generates the energy beam. In some embodiments, controllingcomprises feedback, feed-forward, closed loop, or open loop control. Insome embodiments, controlling comprises real time control during (b). Insome embodiments, real time comprises during formation of (i) the layerof transformed material, (ii) at least several melt pools of theplurality of melt pools, (iii) a single file of melt pools within theplurality of melt pools, or (iv) a melt pool within the plurality ofmelt pools. In some embodiments, the controlling comprises controlling atemperature of exposed surfaces of one or more melt pools of theplurality of melt pools. In some embodiments, the controlling comprisescontrolling a radiation emitted or reflected from exposed surfaces ofthe one or more melt pools of the plurality of melt pools. In someembodiments, the controlling comprises sensing. In some embodiments, thesensing comprises optically or spectroscopically sensing. In someembodiments, the controlling comprises detecting. In some embodiments,the detecting comprises using at least one single pixel detector. Insome embodiments, the detecting comprises priding an electromagneticradiation that is emitted and/or reflected from the exposed surfaces ofthe one or more melt pools of the plurality of melt pools, through anoptical fiber that is operatively coupled to a detector.

In another aspect, a system for printing a three-dimensional objectcomprises: an enclosure that is configured to accommodatepre-transformed material; a first energy source that is configured togenerate a first energy beam that transforms a first portion of thepre-transformed material to form a first section of thethree-dimensional object, which first section comprises a first materialcharacteristic, wherein the first energy beam is operatively coupled tothe enclosure; a second energy source that is configured to generate asecond energy beam that transforms a second portion of thepre-transformed material to form a second section of thethree-dimensional object, which second section comprises a secondmaterial characteristic that is different from the first materialcharacteristic, wherein the second energy beam is operatively coupled tothe enclosure; and at least one controller that is operatively coupledto the first and second energy beams, which at least one controller iscollectively or separately programmed to perform the followingoperation: operation (i) direct the first energy beam to transform thefirst portion of the pre-transformed material to a form a first sectionin a layer of the three-dimensional object, operation (ii) direct thesecond energy beam to transform the second portion of thepre-transformed material to a form a second section in the layer of thethree-dimensional object.

In some embodiments, the first and second material characteristicscomprise at least one of density, porosity, or microstructure. In someembodiments, the at least one controller is further programmed tocontrol the material characteristics (I) in the first section, (II) inthe second section, or both (III) in the first section and in the secondsection. In some embodiments, the microstructure comprises metallurgicalphase. In some embodiments, the microstructure comprises an averagefundamental length scale of melt pools. In some embodiments, the firstenergy source and the second energy source are the same energy source.In some embodiments, the first energy source and the second energysource are different energy sources. In some embodiments, the firstenergy source and the second energy source are different energy beams.In some embodiments, the first energy beam and the second energy beamare the same energy beam that differ in at least one energy beamcharacteristic. In some embodiments, the energy beam characteristiccomprises at least one of a velocity, a cross section, a power density,a fluence, a duty cycle, a dwell time, a focus, a delay time, or acontinuity of movement. In some embodiments, the first energy beam isconfigured to emit radiation having a smaller cross section as comparedto the second energy beam. In some embodiments, the first energy beam isconfigured to irradiate at a higher power density as compared to thesecond energy beam. In some embodiments, the first energy beam isconfigured to irradiate at a shorter dwell time at a position ascompared to the second energy beam. In some embodiments, the firstenergy beam is configured to continuously move, whereas second energybeam is configured to be stationary and move interchangeably. In someembodiments, the first energy beam is configured to be focused, whereasthe second energy beam is configured to be de-focused.

In another aspect, an apparatus for three-dimensional printing of atleast one three-dimensional object comprises at least one controllerthat is collectively or separately programmed to perform the followingoperations: operation (i) direct a first enemy beam to transform a firstportion of a pre-transformed material to a form a first section in alayer of the at least one three-dimensional object, which first sectioncomprises a first material characteristic, wherein the pre-transformedmaterial is disposed in an enclosure, and; and operation (ii) direct asecond energy beam to transform a second portion of the pre-transformedmaterial to a form a second section in the layer of the at least onethree-dimensional object, which second section comprises a secondmaterial characteristic that is different from the first materialcharacteristic, wherein the second energy beam is operatively coupled tothe enclosure.

In another aspect, printing a three-dimensional object comprises:printing a plurality of layers of transformed material as part of thethree-dimensional object, wherein printing at least one of the pluralityof layers of transformed material comprises: (a) forming a core portionusing a first energy beam that transforms a first pre-transformedmaterial to a first transformed material that hardens into a firsthardened material at a first hardening rate; and (b) forming a skinportion using a second energy beam that transforms a secondpre-transformed material to a second transformed material that hardensinto a second hardened material at a second hardening rate that isslower than the first hardening rate.

In some embodiments, one or more of the plurality of layers oftransformed material defines a layering plane. In some embodiments, analignment line is substantially orthogonal to the layering plane and/oris parallel to an exposed surface of the skirt. In some embodiments,grains of the second set of grains are aligned and/or lean towards thealignment line. In some enthodiments, the first hardening rate resultsin formation of a first set of grains. In some embodiments, the secondhardening rate results in formation of a second set of grains having atleast one varied grain characteristic as compared to the first set ofgrains. In some embodiments, the first and second set of grains comprisemetallurgical microstructures, or crystals. In some embodiments, the atleast one varied grain characteristic comprises an organization ofcrystal structure, crystal phase, grain types, material makeup, oraverage fundamental length scale (e.g., width or length) of the firstand second set of grains. In some embodiments, the second hardenedmaterial comprises a surface, wherein a plurality of grain structures inthe second set of grains are directed to an alignment line that isparallel to the surface and/or to the surface. In some embodiments, thesecond hardened material comprises a melt pool. In some embodiments, themelt pool defines an alignment line that runs through a central portionof the melt pool. In some embodiments, a plurality of grain structuresin the second set of grains converge along the alignment line. In someembodiments, one or more of the plurality of layers of transformedmaterial defines a layering plane. In some embodiments, the alignmentline is (e.g., substantially) orthogonal to the layering plane. In someembodiments, the second set of grains has (i) more organized grains,and/or (ii) grains with a larger average fundamental length scale (e.g.,width or length), as compared to respective ones of the first set ofgrains. In some embodiments, the more organized grains comprise largercoherence length or larger crystals. In some embodiments, the skinportion comprises an exterior surface corresponding to at least afraction of an exterior surface of the three-dimensional object. In someembodiments, (b) comprises forming at least one tile. In someembodiments, the second energy beam is substantially stationary during adwell time. In some embodiments, (b) comprises forming a plurality oftiles by: (I) transforming the second pre-transformed material to thesecond transformed material at a first position on a target surfaceusing the second energy beam during a first time period to form a firsttile, which first position is along a path-of-tiles, wherein during thefirst time period, the second energy beam is stationary or substantiallystationary (e.g., such that it at most undergoes pendulum and/orcircular movement about the first position); (II) translating the secondenergy beam to a second position on the target surface along thepath-of-tiles, which second position is different from the firstposition, wherein the second energy beam is translated during anintermission without transforming the second pre-transformed materialalong the path-of-tiles; and (III) repeating (I) and (II) to an end ofthe path-of-tiles. In some embodiments, the energy beam is irradiated inaccordance with a power density profile characterized as having a (e.g.,substantially) constant power density period followed by a decreasingpower density period. In some embodiments, the period in which the powerdensity of the energy beam is decreasing occurs at an end of anirradiation time. In some embodiments, during an irradiation time of thesecond energy beam, a power density of the second energy beam isconstant or pulsing. In some embodiments, the method further comprisesforming a plurality of tiles by moving the second energy beam todifferent locations of the second pre-transformed material in accordancewith a path. In some embodiments, the method further comprises turningoff an energy source that generates the first energy beam during movingof the first energy beam between the different locations. In someembodiments, the tiles of the plurality of tiles overlap with eachother. In some embodiments, (a) comprises forming a plurality of hatchesby continuously moving the first energy beam along a pre-transformedmaterial in accordance with a path. In some embodiments, the pluralityof layers of transformed material comprises a first and second layer. Insome embodiments, the first layer is characterized by a first melt poolthat defines a first alignment line. In some embodiments, a second layeris characterized by a second melt pool that defines a second alignmentline. In some embodiments, the first alignment line is (e.g.,substantially) parallel to the second alignment line. In someembodiments, the alignment line is (e.g., substantially) parallel to agrowth direction of the three-dimensional object during printing. Insome embodiments, the core portion comprises a first grain. In someembodiments, the skin portion comprises a second grain that is longerthan the first grain. In some embodiments, core portion comprises aplurality of first grains characterized as having a first average grainfundamental length scale. In some embodiments, the skin portioncomprises a plurality of second grains characterized as having a secondaverage grain fundamental length scale different than the first averagegrain fundamental length scale. In some embodiments, the first andsecond energy beams are generated by the same energy source. In someembodiments, the first and second energy beams are generated bydifferent energy sources. In some embodiments, printing the plurality oflayers of transformed material comprises forming a plurality of skinportions in accordance with the exterior surface of a three-dimensionalobject. In some embodiments, at least one characteristic of the firstenergy beam is different than a respective at least one characteristicof the second energy beam. In some embodiments, the at least onecharacteristic of the first or second energy beam comprisestranslational speed, cross section, dwell time, intermission time,pulsing frequency, power density, power density profile over time, ortranslational scheme (e.g., tiling or hatching). In some embodiments, apower density of the first energy beam is greater than a power densityof the second energy beam. In some embodiments, a scan speed of thesecond energy beam slower than a scan speed of the first energy beam.

In another aspect, printing a three-dimensional object comprises one ormore controllers that are individually or collectively programmed to:direct a first energy beam and a second energy beam to print a pluralityof layers of transformed material as part of the three-dimensionalobject, wherein the one or more controllers is programed to: (a) directthe first energy beam to transforms a first pre-transformed material toa first transformed material that hardens into a first hardened materialat a first hardening rate to form a core portion; and (b) direct thesecond energy beam to transform a second pre-transformed material to asecond transformed material that hardens into a second hardened materialat a second hardening rate that is slower than the first hardening rateto form a skin portion.

In some embodiments, the one or more controllers is programed to directthe first energy beam to form the first transformed material having thefirst hardening rate that results in formation of a first set of grains.In some embodiments, the at least one controller is programed to directthe second energy beam to form the second transformed material havingthe second hardening rate results in formation of a second set of grainshaving at least one varied grain characteristic as compared to the firstset of grains. In some embodiments, grains of the first and second setof grains comprise metallurgical microstructures, or crystals. In someembodiments, the at least one varied grain characteristic comprises anorganization of crystal structure, crystal phase, grain types, materialmakeup, or average fundamental length scale (e.g., width or length) ofgrains of the first and second set of grains. In some embodiments, theone or more controllers is programed to direct (I) a first energy sourceto generate the first energy beam, and (ii) direct a second energysource to generate the second energy beam. In some embodiments, thefirst energy source is the same as the second energy source. In someembodiments, the first energy source is different than the second energysource. In some embodiments, the one or more controllers controls atleast one characteristic of the first energy beam, the second energybeam, the first energy source and/or the second energy source. In someembodiments, the one or more controllers controls at least onecharacteristic of the first energy beam and/or the second energy beam atleast partially based on data from one or more sensors. In someembodiments, the one or more sensors collect temperature, optical, orspectroscopic data. In some embodiments, the one or more sensors detectelectromagnetic radiation that is emitted and/or reflected from anexposed surface of one or more melt pools formed during (a) and/or (b).In some embodiments, the one or more controllers directs feedback orclosed loop control. In some embodiments, the one or more controllersdirects feed-forward or open loop control. In some embodiments, the oneor more controllers is programmed to direct the second energy beam toform at least one tile during directing the second energy beam in (b).In some embodiments, forming the at least one tile comprises directingthe second energy beam at the second pre-transformed material for adwell time of at least about 0.1 milliseconds. In some embodiments, theone or more controllers is programed to direct a substantiallystationary energy beam during the dwell time (e.g., whereinsubstantially stationary comprises movement (e.g., circular or pendulum)that does not exceed a fundamental length scale of a footprint of thesecond energy beam on time second pre-transformed material about apoint). In some embodiments, the one or more controllers is programmedto direct the second energy beam to form a plurality of tiles by movingthe second energy beam to different locations of a pre-transformedmaterial in accordance with a path. In some embodiments, the one or morecontrollers is programmed to direct turning off an energy source thatgenerates the second energy beam during moving of the second energy beambetween the different locations. In some embodiments, the one or morecontrollers is programmed to direct the same energy source to generatethe first and second energy beams. In some embodiments, the one or morecontrollers is programmed to direct different energy sources to generatethe first and second energy beams. In some embodiments, the one or morecontrollers includes at least two controllers. In some embodiments, theone or more controllers is programmed to direct the first and secondenergy beams to have different power densities. In some embodiments, apower density of the second energy beam is greater than a power densityof the first energy beam. In some embodiments, a power density of thesecond energy beam is lower than a power density of the first energybeam. In some embodiments, the one or more controllers is programmed todirect adjusting one or more characteristics of the first energy beamand/or the second energy beam before, during or after directing thefirst energy beam in (a) and/or directing the second energy beam in (b).In some embodiments, the one or more characteristics comprisetranslational speed, cross section, dwell time, intermission time,pulsing frequency, power density, power density profile over time, ortranslational scheme (e.g., tiling or hatching). In some embodiments,the one or more characteristics of the first energy beam and/or thesecond energy beam is adjusted to accomplish a different solidificationrate during directing the second energy beam in (b) compared to duringdirecting the first energy beam in (a).

In another aspect, a method for printing a three-dimensional objectcomprises: (a) using a first energy beam to transform a first portion ofa pre-transformed material to a form a first section in a layer of thethree-dimensional object, which first section comprises a first materialcharacteristic, wherein the pre-transformed material is disposed in anenclosure, and wherein the first energy beam is operatively coupled tothe enclosure; and (b) using a second energy beam to transform a secondportion of the pre-transformed material to a form a second section inthe layer of the three-dimensional object, which second sectioncomprises a second material characteristic that is different from thefirst material characteristic, wherein the second energy beam isoperatively coupled to the enclosure.

In another aspect, a computer software product for three-dimensionalprinting of at least one three-dimensional object, comprises anon-transitory computer-readable medium in which program instructionsare stored., which instructions, when read by a computer, cause thecomputer to perform operations comprising: operation (a) directing afirst energy beam to transform a first portion of a pre-transformedmaterial to a form a first section in a layer of the at least onethree-dimensional object, which first section comprises a first materialcharacteristic, wherein the pre-transformed material is disposed. In anenclosure, and wherein the first energy beam is operatively coupled tothe enclosure; and operation (b) directing a second energy beam totransform a second portion of the pre-transformed material to a form asecond section in the layer of the at least one three-dimensionalobject, which second section comprises a second material characteristicthat is different from the first material characteristic, wherein thesecond energy beam is operatively coupled to the enclosure.

In another aspect, a method for printing a three-dimensional object, themethod comprises: transforming at least a portion of a first hardenedmaterial to a second hardened material by directing an energy beam alonga path on an exposed surface of the first hardened material, the atleast a portion of the first hardened material having a first density,wherein transforming comprises generating one or more melt pools in theat least a portion of the first hardened material, wherein the secondhardened material has a second density greater than the first density ofthe first hardened material.

In some embodiments, the first hardened material is generated bytransforming a pre-transformed material to one or more layers of atransformed material as part of the first hardened material. In someembodiments, the pre-transformed material comprises elemental metal,metal alloy, ceramic, or an allotrope of elemental metal. In someembodiments, the pre-transformed material comprises a particulatematerial. In some embodiments, the energy beam is a second energy beam,the method further comprises, prior to directing the second energy beam,using a first energy beam to transform a pre-transformed material to atransformed material as part of the first hardened material. In someembodiments, the method further comprises prior to directing the secondenergy beam, forming the first hardened material by directing a firstenergy beam on an exposed surface of a material bed that includes thepre-transformed material. In some embodiments, the first energy beam hasthe same energy density as the second energy beam. In some embodiments,the first energy beam has different energy density than the secondenergy beam. In some embodiments, the at least a portion comprises oneor more layers of hardened material. In some embodiments, the at least aportion comprises a plurality of layers. In some embodiments, theplurality of layers comprises successive layers. In some embodiments,the one or more melt pools are successively formed. In some embodiments,the one or more melt pools is characterized as having an isotropicaspect ratio or a non-isotropic aspect ratio, in some embodiments, thenon-isotropic aspect ratio is a high aspect ratio. In some embodiments,the first density is at most about 94.5%. In some embodiments, thesecond density is at least about 95%. In some embodiments, the seconddensity is at least about 99.5%. In some embodiments, the second densityis at least about 99.9%. In some embodiments, the first hardenedmaterial has a first surface roughness and the second hardened materialhas a second surface roughness that is lower than the first surfaceroughness of the first hardened material. In some embodiments, thesecond surface roughness is measured as having an Ra of less than about40 μm. In some embodiments, the second surface toughness is measured athaving an Ra of less than about 20 μm. In some embodiments, the methodfurther comprises: before directing the energy beam, placing apre-transformed material on the first hardened material. In someembodiments, the pre-transformed material is (i) transformed duringtransformation of the at least a portion of a first hardened material toa second hardened material, and (ii) contacts the at least a portion ofthe first hardened material to form the second hardened material. Insome embodiments, the portion of the first hardened material comprisesfrom 2 to 15 layers. In some embodiments, prior to directing the energybeam, the at least a portion of the first hardened material has avertical height of at least about 500 micrometers. In some embodiments,an average depth of the one or more melt pools is at least about 1.5times larger than an average width of a vertical cross section of theone or more melt pools. In some embodiments, the method furthercomprises after directing the energy beam, forming one or moreadditional layers of a third hardened material on the second hardenedmaterial. In some embodiments, the at least a portion of the firsthardened material is part of a horizontally non-overlapping portion ofthe part. In some embodiments, the horizontally non-overlapping portionforms at least a segment of an overhang or a cavity ceiling as part ofthe three-dimensional object. In some enthodiments, the overhang orcavity ceiling forms an angle with respect to a platform adjacent towhich a material bed is disposed, wherein the angle is (i) from zero tothirty degrees or (ii) from 150 to 180 degrees. In some embodiments, theangle is (i) from zero to fifteen degrees or (ii) from 175 to 180degrees. In some embodiments, the first hardened material comprises anelemental metal, metal alloy, ceramic, or an allotrope of elementalmetal.

In another aspect, an apparatus for three-dimensional printing of atleast one three-dimensional object comprises at least one controllerthat is collectively or separately programmed to direct an energy beamto transform at least a portion of a first hardened material to a secondhardened material, the at least a portion of the first hardened materialhaving a first density, wherein transforming comprises generating one ormore melt pools in the at least a portion of the first hardenedmaterial, wherein directing the energy beam to transform comprisesdirecting the energy beam along a path on an exposed surface of thefirst hardened material, and wherein the second hardened material has asecond density greater than the first density of the first hardenedmaterial.

In some embodiments, the energy beam comprises an electromagnetic orcharged particle beam. In some embodiments, the energy beam comprises alaser beam. In some embodiments, the first density is at most about 94%.In some embodiments, the second density is at least about 95%. In someembodiments, the at least a portion of the first hardened material has afirst surface roughness, and wherein the second hardened material has asecond surface roughness that is less than the first surface roughnessof the first hardened material. In some embodiments, the second surfaceroughness is measured as having an Ra of less than about 40 micrometers.In some embodiments, the second surface roughness is measured at havingan Ra of less than about 20 micrometers. In some embodiments, the atleast one controller is further configured to direct disposal of apre-transformed material layer on the first hardened material prior todirecting the energy beam to transform the at least the portion of thefirst hardened material to the second hardened material. In someembodiments, during transformation of the at least the portion of thefirst hardened material to the second hardened material, the at leastone controller further directs the energy beam to transform thepre-transformed material to a transformed material that forms a part ofthe second hardened material. In some embodiments, the energy beam is asecond energy beam, and wherein at least one controller is furtherconfigured to direct a first energy beam to transform a pre-transformedmaterial to a transformed material to form the first hardened material.In some embodiments, the first hardened material is formed in alayerwise fashion. In some embodiments, the first energy beam and thesecond energy beam are different. In some embodiments, the first energybeam and the second energy beam are the same energy beam. In someembodiments, the first energy beam and the second energy beam originatefrom the same energy source. In some embodiments, the first energy beamand the second energy beam originate from the different energy sources.In some embodiments, the first hardened material has an average densityof at most about 60%. In some embodiments, the first hardened materialhas an average density of at most about 90%. In some embodiments, thefirst hardened material comprises between 2 and 15 layers. In someembodiments, the first hardened material (e.g., a layer of hardenedmaterial) has a thickness of about 100 micrometers and 800 micrometers.In some embodiments, an average depth of the one or more melt pools islarger than an average width of a vertical cross section of the one ormore melt pools, which larger is by at least about 1.5 times. In someembodiments, the at least one controller is further configured to directformation of one or more layers of additional hardened material on thesecond hardened material. In some embodiments, the one or more layers ofadditional hardened material are part of a horizontally non-overlappingportion as part of the at least one three-dimensional object. In someembodiments, the horizontally non-overlapping portion forms at least asegment of an overhang or a cavity ceiling. In some embodiments, theoverhang or cavity ceiling form an angle with an exposed surface of amaterial bed and/or with a platform above which the material bed isdisposed, wherein the angle is from zero to thirty degrees. In someembodiments, the angle is from zero to fifteen degrees. In someembodiments, the overhang or cavity ceiling forms an angle with respectto a platform adjacent to which a material bed is disposed, wherein theangle is (i) from zero to thirty degrees or (ii) from 150 to 180degrees. In some embodiments, the angle is (i) from zero to fifteendegrees or (ii) from 175 to 180 degrees. In some embodiments, the atleast one controller comprise a control scheme. In some embodiments, theat least one controller comprise a control scheme, wherein the controlscheme comprises open loop or closed loop control. In some embodiments,the at least one controller comprise a control scheme, wherein thecontrol scheme comprises feedback or feed forward control. In someembodiments, the at least one controller comprise a control scheme,wherein the control scheme uses a signal from at least one sensor. Insome embodiments, the at least one controller comprise a control scheme,wherein the control scheme uses a signal from at least one sensor,wherein the sensor measures one or more properties of a surface portionthat is irradiated by the first and/or second energy beam or a vicinityof that surface portion. In some embodiments, the at least onecontroller comprise a control scheme, wherein the control scheme uses asignal from at least one sensor, wherein the sensor measures one or moreproperties of a surface portion that is irradiated by the first and/orsecond energy beam or a vicinity of that surface portion, wherein thevicinity is at most about six diameters of a cross section of the firstand/or second energy beam. In some embodiments, the at least onecontroller comprise a control scheme, wherein the control scheme uses asignal from at least one sensor, wherein the sensor measures one or moreproperties of a surface portion that is irradiated by the first and/orsecond energy beam or a vicinity of that surface portion, wherein thevicinity is at most about six FLS of the surface portion that isirradiated by the first and/or second energy beam. In some embodiments,the at least one controller comprise a control scheme, wherein thecontrol scheme comprises an algorithm. In some embodiments, the at leastone controller comprise a control scheme, wherein the control schemecomprises an algorithm, wherein the algorithm includesthermo-mechanical, or geometric properties of the at least the portionof the first hardened material and/or the second hardened material. Insome embodiments, the at least one controller comprise a control scheme,wherein the control scheme comprises an algorithm, wherein the algorithmincludes material properties of the at least the portion of the firsthardened material and/or the second hardened material. In someembodiments, the at least one controller comprise a control scheme,wherein the control scheme comprises an algorithm, wherein the algorithmincludes material properties of the at least the portion of the firsthardened material and/or the second hardened material,

In another aspect, a three-dimensional object comprises: a plurality oflayers of hard material that are stacked and bonded together to form ashape of the three-dimensional object, which plurality of layers ofhardened material comprises: a core characterized as having a firstmicrostructure comprising a first plurality of grains associated withbeing formed at a first solidification rate; and a skin portion coupledwith the core, which skin portion comprises: (i) a second microstructurecomprising a second plurality of grains associated with being formed ata second solidification rate that is different than the firstsolidification rate, and (ii) an exterior surface corresponding to atleast a fraction of an exterior surface of the three-dimensional object.

In some embodiments, a layer of the skin portion comprises a melt poolwhich is a width of the skin. In some embodiments, the skin portion isat least a fraction of the skin of the three-dimensional object. In someembodiments, grains of the second plurality of grains are aligned andgrains of the first plurality of grains are misaligned. In someembodiments, the skin comprises at least one melt pool that defines analignment line that runs through a central portion of the at least onemelt pool. In some embodiments, the alignment line is parallel to or atthe exterior surface. In some embodiments, with respect to the alignmentline: the second plurality of grains are aligned, and the firstplurality of grains are misaligned. In some embodiments, the first orsecond plurality of grains comprises a crystal. In some embodiments, thefirst or second plurality of grains comprises a metallurgicalmicrostructure. In some embodiments, the metallurgical microstructurecomprises a dendrite or a cell. In some embodiments, the first or secondplurality of grains align at a non-zero angle along, the alignment line.In some embodiments, the first plurality of grains is different from thesecond plurality of grains by at least one aspect comprising afundamental length scale, chemical makeup, crystal structure,metallurgical microstructure:, coherence length, grain size, or spatialplacement relative to the alignment line. In some embodiments, thesecond plurality of grains have a larger fundamental length scale,coherence length, grain size, and/or more organized spatial placementrelative to the alignment line compared to the first plurality ofgrains. In some embodiments, the first microstructure is characterizedby a first grain. In some embodiments, the second microstructure ischaracterized by a second grain that has at least one aspect that isdifferent from the first grain. In some embodiments, the aspectcomprises a fundamental length scale, chemical makeup, crystalstructure, metallurgical microstructure, or spatial placement in a meltpool relative to the alignment line. In some embodiments, thefundamental length scale comprises a length or a width. In someembodiments, the first microstructure is characterized by a first set ofgrains. In some embodiments, the second microstructure is characterizedby a second set of grains. In some embodiments, an average length and/orwidth of the second set of grains that is longer and/or widerrespectively than an average length of the first set of grains. In someembodiments, an average fundamental length scale of the second set ofgrains is about 1.5 times greater than an average fundamental lengthscale of the first set of grains. In some embodiments, the core is aninterior of the three-dimensional object. In some embodiments, the skinis (e.g., chemically (e.g., metallically)) bonded with the core. In someembodiments, the skin has a thickness ranging from about 20 micrometersto about 1000 micrometers. In some embodiments, the thickness rangesfrom about 20 micrometers to about 400 micrometers. In some embodiments,the skin comprises at least one melt pool. In some embodiments, the skinhas a thickness of at most about twice a width of the at least one meltpool. In some embodiments, the second solidification rate is slower thanthe first solidification rate. In some enthodiments, secondsolidification rate is faster than the first solidification rate. Insome embodiments, the first solidification rate is associated with afirst cooling rate. In some embodiments, the second solidification rateis associated with a second cooling rate different than the firstcooling rate. In some embodiments, the core comprises a first set ofmelt pools. In some embodiments, the skin comprises a second set of meltpools. In some embodiments, an orientation of the second set of grainsis with respect to the second set of melt pools and/or the exteriorsurface of the skin. In some embodiments, melt pools of the second setof melt pools are aligned with the exterior surface of the skin. In someembodiments, the exterior surface of the skin has an area surfaceroughness (Sa) of at most about 50 micrometers. In some embodiments, theexterior surface of the skin has an area surface roughness (Sa) of atmost about 20 micrometers. In some embodiments, the exterior surface ofthe skin has an area surface roughness (Sa) of at most about 10micrometers. In some embodiments, the skin is characterized by aplurality of tiles. In some embodiments, centers of adjacent (e.g.,successive) tiles are (e.g., substantially) uniformly spaced apart fromone another. In some embodiments, at least two adjacent (e.g.,successive) tiles overlap with each other. In some embodiments, thecenters of adjacent tiles are spaced apart a distance ranging betweenabout 10 micrometers and about 500 micrometers. In some embodiments, theskin comprises a melt pool comprising a curved bottom portion indicativeof a stacking vector in which the plurality of layers are bondedtogether. In some embodiments, the stacking vector is (e.g.,substantially) perpendicular to a layering plane of thethree-dimensional object. In some embodiments, the melt pool defines analignment line that runs through a central portion of the melt pool. Insome embodiments, the stacking vector is (e.g., substantially) parallelto the alignment line. In some embodiments, crystal structures of themelt pool converge in a V-shape. In some embodiments, a top of theV-shape is pointed in accordance with the stacking vector. In someembodiments, the exterior surface of the skin has a plurality ofcrescent-shaped ridges corresponding to overlapping tiles.

In another aspect, a three-dimensional object comprises: a corecomprising a first plurality of layers of hardened materialcharacterized as having a first microstructure associated with beingformed at a first solidification rate; and a skin coupled with the coreand comprising a second plurality of layers of hardened material,wherein: (i) an exterior surface of the skin corresponds to at least afraction of an exterior surface of the three-dimensional object, and(ii) the second, plurality of layers of hardened material ischaracterized as having a second microstructure associated with beingformed at a second, solidification rate that is different than the firstsolidification rate.

In some embodiments, the first solidification rate is associated with acooling rate of the first hardened material. In some embodiments, thesecond solidification rate is associated with a cooling rate of thesecond hardened material. In some embodiments, the first solidificationrate is slower than the second solidification rate. In some embodiments,the first solidification rate is faster than the second solidificationrate. In some embodiments, the first microstructure comprises a firstmelt pool or a first grain. In some embodiments, the secondmicrostructure comprise a second melt pool or a second grain. In someembodiments, the first grain comprises a first constituent and whereinthe second grain comprises a second constituent. In some embodiments,the first constituent differs from the second constituent in at leastone aspect comprising: fundamental length scale, chemical makeup,crystal structure, metallurgical microstructure, or spatial placement ina melt pool. In some embodiments, the first constituent comprises afirst crystal or a first metallurgical microstructure. In someembodiments, the second constituent comprises a second crystal or asecond metallurgical microstructure. In some embodiments, themetallurgical microstructure comprises a dendrite, or a cell. In someembodiments, the skin has a thickness ranging from about 20 micrometersto about 1000 micrometers. In some embodiments, grains of the secondmicrostructure of the skin are more organized as compared to grains ofthe first microstructure of the core. In some embodiments, grains of thesecond microstructure of the skin aligned with respect to (i) theexterior surface of the skin and/or (ii) an interior of a melt pool. Insome embodiments, the skin comprises (i) a melt pool that defines analignment line that runs parallel to the exterior surface of the skinand/or through a central portion of the melt pool, and (ii) a pluralityof grain structures that are directed to (e.g., converge towards) thealignment line. In some embodiments, grains of the second microstructureare aligned at an angle with respect to the alignment line. In someembodiments, the first or second grain comprises dendrite, or cell. Insome embodiments, adjacent layers of the first and second plurality oflayers are chemically (e.g., metallically) bonded with one another. Insome embodiments, the skin has a thickness ranging from about 20micrometers to about 400 micrometers. In some embodiments, the skin ischaracterized by (i) a melt pool that defines an alignment line thatruns through a central portion of the melt pool, and (ii) a plurality ofgrain strictures that converge along the alignment line. In someembodiments, at least two of the plurality of grain structures in themelt pool converge at a non-zero angle. In some embodiments, the corecomprises a first set of grains. In some embodiments, the skin comprisesa second set of grains. In some embodiments, grains of the second sethave a larger fundamental length scale (e.g., on average) than grains ofthe first set. In some embodiments, the fundamental length scalecomprises a width or a length. In some embodiments, the skin is (e.g.,chemically (e.g., metallically)) bonded with the core. In someembodiments, the skin comprises dendrites that are orientedsubstantially parallel to the alignment line. In some embodiments,substantially parallel comprises at an angle of at most about twentydegrees with respect to the alignment line. In some embodiments, grainsof the second set are (e.g., on average) about 1.5 times thicker thangrains of the first set. In some embodiments, the first and secondplurality of layers comprise a metal. In some embodiments, the metalcomprises an elemental metal or a metal alloy. In some embodiments, themetal alloy is an iron comprising alloy, a nickel comprising alloy, acobalt comprising allow, a chrome comprising alloy, a cobalt chromecomprising alloy, a titanium comprising alloy, a magnesium comprisingalloy, or a copper comprising alloy. In some embodiments, thethree-dimensional object comprises a plurality of stacked layers ofhardened material. In some embodiments, stacked layers are boundtogether to form a shape of the three-dimensional object. In someembodiments, the skin is characterized by a plurality of tiles. In someembodiments, centers of adjacent tiles are (e.g., substantially)uniformly spaced apart from one another. In some embodiments, at leasttwo adjacent tiles overlap with each other. In some embodiments, thecenters of adjacent tiles are spaced apart a distance ranging betweenabout 10 micrometers and about 500 micrometers. In some embodiments, thecenters of adjacent tiles are spaced apart a distance ranging betweenabout 50 micrometers and about 500 micrometers. In some embodiments, alayering, plane is defined between two successive layers of the firstand/or second plurality of layers. In some embodiments, the skin is abottom skin of an overhang structure of the three-dimensional object. Insome embodiments, a vector normal to a the exterior surface of thebottom skin that intersects (1) the layering plane or to (2) a planeparallel to the layering plane, forms an angle with respect to thelayering plane or with a line parallel to the layering plane thatintersects with the vector. In some embodiments, the angle is at leastabout sixty degrees at most about ninety degrees, wherein the vector isdirected towards the skin. In some embodiments, angle is no greater thanabout ten degrees In some embodiments, the exterior surface has ameasured area surface roughness (Sa) at most about 20 micrometers. Insome embodiments, the exterior surface has a measured area surfaceroughness (Sa) at most about 5 micrometers. In some embodiments, thecore has the same or substantially the same chemical composition as theskin. In some embodiments, the exterior surface of the skin has aplurality of crescent-shaped ridges corresponding to overlapping tiles.

In another aspect, a three-dimensional object comprises: a plurality oflayers of hardened material that are bonded together to form a shape ofthe three-dimensional object, wherein the plurality of layers comprises:an interior (e.g., core) portion of the three-dimensional object; and askin portion that is bonded with the interior portion and comprising asecond plurality of layers, wherein: (i) an exterior surface of the skinportion corresponds to at least a fraction of an exterior surface of thethree-dimensional object, and (ii) the exterior surface of the skinportion comprises a repetitive microstructure (e.g., a micro-texture oftwo-dimensional array of periodic peaks and valleys).

In some embodiments, the repetitive microstructure is repetitive in alayer of hardened material. In some embodiments, the array is periodicin at least one dimension. In some embodiments, the array is periodicalong a layer of the hard material. In some embodiments, the repetitivemicrostructure comprises a series of peaks and valleys. In someembodiments, the array is locally repetitive on the exterior surface ofthe skin. In some embodiments the array is repetitive in both of itstwo-dimensions. In some embodiments, a depth of a valley (e.g., or anaverage depth of a number of valleys) is at most about 20 micrometers.In some embodiments, the two-dimensional array comprises overlappingtiles of deposited material. In some embodiments, the overlapping tilesappear as crescent shapes. In some embodiments, the valley immediatelyfollows a peak. In some embodiments, the repetitive microstructure issequentially repetitive. In some embodiments, the repetitivemicrostructure corresponds to scales. In some embodiments, the scalesare overlapping and appear as crescent shapes. In some embodiments, theoverlapping tiles are arranged in rows of tiles. In some embodiments,adjacent tiles in a row overlap by at least about five percent. In someembodiments, adjacent tiles in a row overlap by at most about 98percent. In some embodiments, centers of adjacent tiles in a row are adistance of at least about 5 micrometers. In some embodiments, centersof adjacent tiles in a row are at a distance of at most about 1000micrometers. In some embodiments, a first row of tiles overlaps withtiles of a second row of tiles that is successive to the first row oftiles. In some embodiments, the first row of tiles overlaps with thesecond row of tiles by at least about five percent. In some embodiments,the first row of tiles overlaps with the second row of tiles by at mostabout 98 percent. In some embodiments, a distance between a center of afirst tile of the first row of tiles and a center of a second tile ofthe second row of tiles is at least about 5 micrometers. In someembodiments, a distance between a center of a first tile of the firstrow of tiles and a center of a second tile of the second row of tiles isat most about 1000 micrometers. In some embodiments, tiles within thefirst row of tiles overlap by a first distance. In some embodiments,tiles of the first row of tiles overlap with tiles of the second row oftiles by a second distance greater than the first distance. In someembodiments, tiles within the first row of tiles overlap by a firstdistance. In some embodiments, tiles of the first row of tiles overlapwith tiles of the second row of tiles by a second distance less than thefirst distance. In some embodiments, the overlapping tiles have anaverage fundamental length scale of a least about 50 micrometers. Insome embodiments, the overlapping tiles have an average fundamentallength scale of a most about 1000 micrometers. In some embodiments, theinterior portion is characterized as having a first grain structureassociated with being formed at a first solidification rate. In someembodiments, the skin portion is characterized as having a second grainstructure associated with being formed at a second solidification ratethat is different than the first solidification rate. In someembodiments, the first solidification rate is greater than the secondsolidification rate. In some embodiments, the first solidification rateis less than the second solidification rate. In some embodiments, theexterior surface of the skin portion has an area surface roughness (Sa)of at most about 30 micrometers. In some embodiments, the exteriorsurface of the skin portion has an area surface roughness (Sa) of atmost about 10 micrometers, in some embodiments, the skin portion and theinterior portion are metallically bonded with each other. In someembodiments, the skin portion comprises a melt pool that defines analignment line that runs through a central portion of the melt pool. Insome embodiments, the melt pool comprises grain structures that convergealong the alignment line in the melt pool. In some embodiments, thegrain structures comprise at least one crystal. In some embodiments, thegrain structures converge at a non-zero angle along the alignment line.In some embodiments, the melt pool comprises a curved bottom portionindicative of a stacking vector in which the plurality of layers arebonded together. In some embodiments, the grain structures converge in aV-shape such that a top of the V-shape is pointed in accordance with thestacking vector. In some embodiments, the interior portion comprises afirst plurality of grains and wherein the skin portion comprises asecond plurality of grains. In some embodiments, grains of the secondplurality of grains are aligned and grains of the first plurality ofgrains are misaligned. In some embodiments, the interior portioncomprises a first plurality of grains and wherein the skin portioncomprises a second plurality of grains. In some embodiments, analignment line that runs through a central portion of a melt pool of theskin, or is parallel to, or at, the exterior surface of the skin. Insome embodiments, with respect to the alignment line: the secondplurality of grains are aligned, and the first plurality of grains aremisaligned. In some embodiments, the second plurality of grains align ata non-zero angle along the alignment line. In some embodiments, thefirst plurality of grains is different from the second plurality ofgrains by at least one aspect comprising a fundamental length scale,chemical makeup, crystal structure, metallurgical microstructure,coherence length, grain size, or spatial placement relative to thealignment line. In some embodiments, the second plurality of grains havea larger:fundamental length scale, coherence length, grain size, and/ormore organized spatial placement relative to the alignment line. In someembodiments, the interior portion comprises a first grain. In someembodiments, the skin portion comprises a second grain that has at leastone aspect that is different from the first grain. In some embodiments,the aspect comprises a fundamental length scale, chemical makeup,crystal structure, metallurgical microstructure, or spatial placement ina melt pool relative to the alignment line.

In another aspect, an apparatus for printing one or more 3D objectscomprises a controller that is programmed to direct a mechanism used ina three-dimensional priming methodology to implement (e.g., effectuate)the method disclosed herein, wherein the controller is operativelycoupled to the mechanism.

In another aspect, a computer software product, comprising anon-transitory computer-readable medium in which program instructionsare stored, which instructions, when read by a computer, cause thecomputer to direct a mechanism used in the three-dimensional primingprocess to implement (e.g., effectuate) any of the method disclosedherein, wherein the non-transitory computer-readable medium isoperatively coupled to the mechanism.

Another aspect of the present disclosure provides a non-transitorycomputer-readable medium comprising machine-executable code that, uponexecution by one or more computer processors, implements any of themethods disclosed herein.

Another aspect of the present disclosure provides a computer systemcomprising one or more computer processors and a non-transitory,computer-readable medium coupled thereto. The non-transitorycomputer-readable medium comprises machine-executable code that, uponexecution by the one or more computer processors, implements any of themethods disclosed herein.

Additional aspects and advantages of the present disclosure will becomereadily apparent to those skilled in this art from the followingdetailed description, wherein only illustrative embodiments of thepresent disclosure are shown and described. As will be realized, thepresent disclosure is capable of other and different embodiments, andits several details are capable of modifications in various obviousrespects, all without departing from the disclosure. Accordingly, thedrawings and description are to be regarded as illustrative in nature,and not as restrictive,

INCORPORATION BY REFERENCE

All publications, patents, and patent applications mentioned in thisspecification are herein incorporated by reference to the same extent asif each individual publication, patent, or patent application wasspecifically and individually indicated to be incorporated by reference.

BRIEF DESCRIPTION OF DRAWINGS

The novel features of the invention are set forth with particularity inthe appended claims. A better understanding of the features andadvantages of the present invention will be obtained by reference to thefollowing detailed description that sets forth illustrative embodiments,in which the principles of the invention are utilized, and theaccompanying drawings or figures (also “FIG.” and “FIGS.” herein), ofwhich:

FIG. 1 shows a schematic side view of a 3D printing system andapparatuses;

FIG. 2 schematically illustrates a path;

FIG. 3 schematically illustrates various paths;

FIG. 4 schematically illustrates an example of a 3D plane;

FIG. 5 schematically illustrates a cross section in portion of a 3Dobject;

FIGS. 6A-6C schematically illustrate a cross section in portion of a 3Dobject;

FIG. 7 schematically illustrates various vertical cross-sectional viewsof various 3D objects;

FIGS. 8A-8B schematically illustrate vertical cross sections of variousmaterial beds;

FIG. 9 schematically illustrates a cross section of a 3D object;

FIG. 10 illustrates a horizontal view of a 3D object;

FIG. 11 schematically illustrates a coordinate system;

FIG. 12 schematically illustrates an optical setup;

FIG. 13 schematically illustrates a computer system;

FIGS. 14A-14B schematically illustrate operations in forming a 3Dobject;

FIGS. 15A-15D schematically illustrate operations in forming a 3Dobject;

FIGS. 16A-16F schematically illustrate operations in forming a 3Dobject;

FIGS. 17A-17F schematically illustrate operations in forming a 3Dobject;

FIGS. 18A-18C schematically illustrate operations in forming a 3Dobject;

FIGS. 19A-19F schematically illustrate operations in forming a 3Dobject;

FIG. 20A schematically illustrates a cross section view of a 3D object;FIG. 20B schematically illustrates a cross section in various portionsof 3D objects;

FIGS. 21A-21B schematically illustrate energy beam patterns o forming aportion of a 3D object;

FIGS. 22A-22D schematically illustrates an energy beam and componentsused in the formation of one or more 3D objects; FIG. 22E schematicallyillustrates a graph associated with a 3D printing process;

FIG. 23 schematically illustrates an optical system used in theformation of one or more 3D objects;

FIG. 24 schematically illustrate a cross section view of a portion of aforming 3D object;

FIG. 25A schematically illustrates a side view of a forming 3D object;FIG. 25B schematically illustrates a temperature profile as a functionof time;

FIGS. 26A-26B schematically illustrate forming at least a portion of a3D object;

FIG. 27 schematically illustrates a graph of power as a function oftime;

FIGS. 28A-28D show schematic top views of various 3D objects;

FIGS. 29A-29E schematically illustrate operations in forming a 3Dobject;

FIGS. 30A-30E schematically illustrate operations in forming a 3Dobject;

FIGS. 31A-31C schematically illustrate graphs depicting power (e.g.,density) as a function of time;

FIGS. 32A-32D schematically illustrate operations in forming a 3Dobject;

FIG. 33 shows a vertical cross section of a 3D object;

FIGS. 34A-34B show vertical cross section images of 3D objects;

FIGS. 35A-35D show various images of 3D objects;

FIGS. 36A-36D show schematic horizontal views of various 3D objects;

FIGS. 37A and 37B schematically illustrate cross section views ofirradiated portions of various 3D objects;

FIGS. 38A and 38B show side and perspective image of 3D objects;

FIG. 39A schematically shows top views of various irradiated portions ofa target surface; and FIGS. 39B and 39C schematically show verticalcross sections in 3D objects;

FIGS. 40A-40C schematically illustrate side views of various operationsin forming a 3D object and various 3D objects;

FIGS. 41A and 41B show perspective views of various 3D objects;

FIGS. 42A and 42B show cross section views of various 3D objects; andFIGS. 42C and 42D schematically illustrate overhang portions of 3Dobjects;

FIGS. 43A-43C schematically illustrate operations in forming 3D objects;

FIGS. 44A-44C schematically illustrate operations in forming 3D objects;

FIG. 45 schematically illustrate operations in forming a 3D object;

FIGS. 46A-46C schematically illustrate operations in forming 3D objects;

FIGS. 47A and 47B show vertical cross sections of 3D objects;

FIG. 48 schematically illustrates a cross section in various layeringplanes;

FIG. 49 shows a cross section view of a 3D object;

FIG. 50 shows a cross section view of a 3D object;

FIG. 51A shows a cross section view of a 3D object with a supportmember, and FIGS. 51B and 51C schematically illustrate different crosssection profiles of a 3D object;

FIGS. 52A and 52B show cross section views of a 3D object;

FIGS. 53A and 53B show cross section views of 3D objects;

FIGS. 54A-54C show cross section views of 3D objects;

FIGS. 55A-55C show cross section views of 3D objects;

FIGS. 56A and 56B show cross section views of 3D objects;

FIGS. 57A-57D show various views of a 3D object;

FIGS. 58A-58D show various views of a 3D object;

FIGS. 59A and 59B show cross section views of a 3D object; and

FIGS. 60A and 60B show cross section views of a 3D object.

The figures and components therein may not be drawn to scale. Variouscomponents of the figures described herein may not be drawn to scale.

DETAILED DESCRIPTION

While various embodiments of the invention have been shown, anddescribed herein, it will be obvious to those skilled in the art thatsuch embodiments are provided, by way of example only. Numerousvariations, changes, and substitutions may occur to those skilled in theart without departing from the invention. It should be understood thatvarious alternatives to the embodiments of the invention describedherein might be employed.

Terms such as “a,” “an” and “the” are not intended to refer to only asingular entity, but include the general class of which a specificexample may be used for illustration. The terminology herein is used todescribe specific embodiments of the invention, but their usage does notdelimit the invention.

When ranges are mentioned, the ranges are meant to be inclusive, unlessotherwise specified. For example, a range between value1 and value2 ismeant to be inclusive and include value1 and value2. The inclusive rangewill span any value from about value1 to about value2. The term“between” as used herein is meant to be inclusive unless otherwisespecified. For example, between X and Y is understood herein to meanfrom X to Y. The term “adjacent” or “adjacent to,” as used herein,includes ‘next to,’ adjoining,“in contact with,' and ‘in proximity to.’In some instances, adjacent to may be ‘above’ or below.” The term“operatively coupled” or “operatively connected” refers to a firstmechanism that is coupled (or connected) to a second mechanism to allowthe intended operation of the second and/or first mechanism.

Fundamental length scale (abbreviated herein as “FLS”) can refer hereinas to any suitable scale (e.g., dimension) of an object. For example, aFLS of an object may comprise a length, a width, a height, a diameter, aspherical equivalent diameter, or a diameter of a bounding sphere.

The methods, systems, apparatuses, and/or software may effectuate theformation of one or more objects (e.g., 3D objects). In some cases, theone or more objects comprise elemental metal or metal alloys. In someembodiments, the 3D object includes an overhang structure. An overhangstructure (also referred to herein as “overhang” or “overhang region”)can refer to a structure of a 3D object that protrudes a distance fromanother structure (e.g., a core structure). An overhang structure maycomprise (e.g., correspond to) a ceiling (e.g., cavity ceiling), bottom(e.g., cavity bottom), protrusion, ledge, blade, hanging structure,undercut, projection, protuberance, balcony, wing, leaf, extension,shelf, jut, hook or step of a 3D object. The overhang may be free ofauxiliary supports during the printing of the overhang. For example, theoverhang may be formed on (e.g., attached to) a previously formed (e.g.,already hardened) portion of the 3D object. A surface (e.g., bottomsurface) of an overhang may have a surface roughness at or below aprescribed roughness measurement.

In some embodiments, the 3D object includes a skin, which can correspondto a portion of the 3D object that includes an exterior surface of the3D object. The skin is sometimes referred to herein as a “rim,”“contour,” “contour portion,” “perimeter,” “perimeter portion,” “outerportion,” or “exterior portion.” In some embodiments, the skin is a“bottom” skin, which can correspond to a skin on a bottom of overhangwith respect to a platform surface during a printing operation.

At times, when forming an overhang structure, and/or other portions ofthe 3D object, adjacent (e.g., two) melt pools may not assume similar(e.g. (e.g., substantially) identical) volume and/or shape due todifferent temperature profiles across the forming melt pool. Suchdissimilarity may lead to the formation of irregular melt pools. Thedifference in volume and/or shape of (e.g., two) adjacent melt pools maybe in the vertical direction. The difference in the volume and/or shapeof the adjacent melt pool may form a stalactite like structure whenextending downwards past the average surface of a bottom skin. Withoutwishing to be bound to theory, several factors may contribute to theirregular melt pools, which factors comprise: gravity, variations insolidification rate of different melt pools, variation in thermal indifferent melt pools, or different mass transfer rate in different meltpools. Dissimilar and/or irregular melt pools may lead to rough,cracked, or balled surfaces (e.g., bottom skin surfaces). Dissimilarand/or irregular melt pools may lead to a deformed hardened material.Dissimilar and/or irregular melt pools may lead to a printed 3D objectthat deviates from its intended purpose.

In some embodiments, at least a portion of a transformed material (e.g.,that forms a hardened material) is being re-melted, during thefabrication of the 3D object. The transformed material may be formed bya 3D printing methodology. In some embodiments, at least a (e.g.,hardened material) melt pool is re-melted during the fabrication of the3D object. The re-melting may be after the melt pool has been at leastpartially hardened (e.g., solidified). In some examples, the re-meltingreduces (e.g., overcomes) formation of irregular and/or dissimilar meltpools (e.g., in the vertical and/or horizontal direction). In someexamples, the re-melting reduces deformation of the 3D object (e.g., asit hardens). In some examples, such re-melting results in a smoother(e.g., bottom skin) surface. Smoother may be of an Ra or Sa value of atmost about 30 μm, 40 μm, 50 μm, 75 μm, or 100 μm. Ra is the arithmeticaverage of a roughness profile. Sa is the arithmetic average of a 3Droughness.

Three-dimensional printing (also referred to herein as “3D printing”)generally refers to a process for generating a 3D object. For example,3D printing may refer to sequential addition of material layer orjoining of material layers (or parts of material layers) to form a 3Dstructure, in a controlled manner. The controlled manner may includeautomated control. In the 3D printing process, the deposited materialcan be transformed (e.g., fused, sintered, melted, bound, or otherwiseconnected) to subsequently harden and form at least a part of the 3Dobject. Fusing (e.g., sintering or melting), binding, or otherwiseconnecting the material is collectively referred to herein astransforming the material (e.g., from a powder material). Fusing thematerial may include melting or sintering the material. Binding cancomprise chemical bonding. Chemical bonding can comprise covalentbonding. Examples of 3D printing include additive printing (e.g., layerby layer printing, or additive manufacturing). 3D printing may includelayered manufacturing. 3D printing may include rapid prototyping. 3Dprinting may include solid freeform fabrication 3D printing may includedirect material deposition. The 3D printing may further comprisesubtractive printing.

3D printing methodologies can comprise extrusion, wire, granular, orpowder bed and inkjet head 3D printing. Extrusion 3D printing cancomprise robo-casting, fused deposition modeling (FDM) or fused filamentfabrication (FFF). Wire 3D printing can comprise electron beam freeformfabrication (EBF3). Granular 3D printing can comprise direct metal lasersintering (DMLS), electron beam melting (EBM), selective laser melting(SLM), selective heat sintering (SHS), laser engineered net shaping(LENS), laser metal deposition (LMD), direct metal deposition (DMD),direct energy deposition (DED), or selective laser sintering (SLS).Powder bed and inkjet head 3D printing can comprise plaster-based 3Dprinting (PP). 3D printing methodologies may differ from methodstraditionally used in semiconductor device fabrication (e.g., vapordeposition, etching, annealing, masking, or molecular beam epitaxy). Insome instances, 3D printing may further comprise one or more printingmethodologies that are traditionally used in semiconductor devicefabrication. 3D printing methodologies can differ from vapor depositionmethods such as chemical vapor deposition, physical vapor deposition, orelectrochemical deposition. In some instances. 3D printing may furtherinclude vapor deposition methods.

The methods, apparatuses, systems, and/or software of the presentdisclosure can be used to form 3D objects for various uses andapplications. Such uses and applications can include, withoutlimitation, electronics, components of electronics (e.g., casings),machines, parts of machines, tools, implants, prosthetics, fashionitems, clothing, shoes, or jewelry. The implants may be directed (e.g.,integrated) to a hard, a soft tissue, or to a combination of hard andsoft tissues. The implants may form adhesion with hard and/or softtissue. The machines may include a motor or motor part. The machines mayinclude a vehicle. The machines may comprise aerospace related machines.The machines may comprise airborne machines. The vehicle may include anairplane, drone, car, train, bicycle, boat, or shuttle (e.g., spaceshuttle). The machine may include a satellite or a missile. The uses andapplications may include 3D objects relating to the industries and/orproducts listed herein.

The present disclosure provides systems, apparatuses, software, and/ormethods for 3D printing of a requested 3D object from a pre-transformed(e.g., powder) material. The object call be pre-ordered, pre-designed,pre-modeled, or designed in real time (i.e., during the process of 3Dprinting). The 3D printing method can be an additive method in which afirst layer is printed., and thereafter a volume of a material is addedto the first layer as separate sequential layer (or parts thereof). Anadditional sequential layer (or part thereof) can be added to theprevious layer by transforming (e.g., fusing (e.g., melting)) a fractionof the pre-transformed material. The transformed (e.g., molten) materialmay harden to form at least a portion of the (hard) 3D object. Thehardening (e.g., solidification) can be actively induced (e.g., bycooling) or can occur without intervention (e.g., naturally). Real timemay be, for example, during the formation of a layer of transformedmaterial, during the formation of a layer of hardened material, duringformation of a portion of a 3D object, during formation of a melt pool,during formation of an entire 3D object, or any combination thereof.

The 3D printing may be performed in an enclosure. During the 3D printing(e.g., during the transformation stage) a pressure of an atmospherewithin the enclosure (e.g., comprising at least one gas) may be anambient pressure. During the formation of the 3D object (e.g., duringthe formation of the layer of hardened material or a portion thereof), aremainder of the material (e.g., powder) bed that did not transform, maybe at an ambient temperature. The ambient temperature may be an averageor mean temperature of the remainder. During the formation of the 3Dobject (e.g., during the formation of the layer of hardened material ora portion thereof), a remainder of the material bed that did nottransform, may not be heated (e.g., actively heated). For example, theremainder may not be heated beyond an (e.g., average or mean) ambienttemperature. During the formation of the 3D object (e.g., during theformation of the layer of hardened material or a portion thereof), aremainder of the material bed that did not transform, may be at atemperature of at most about 10 degrees Celsius (° C.), 20° C., 25° C.,30° C., 40° C., 50° C., 60° C., 70° C., 80° C., 90° C., 100° C., 150°C., 200° C., 250° C., 300° C., 350° C., 400° C., 450° C., 500° C., 550°C., 600° C., 650° C., 700° C., 750° C., 800° C., 850° C., 900° C., or1000° C. During the formation of the 3D object (e.g., during theformation of the layer of hardened material or a portion thereof), aremainder of the material bed that did not transform, may be at atemperature between any of the above-mentioned temperature values (e.g.,from about 10° C. to about 1000° C., from about 100° C. to about 600°C., from about 200° C. to about 500° C. or from about 300° C. to about450° C.). During the formation of the 3D object (e.g., during theformation of the layer of hardened material or a portion thereof), aremainder of the material bed that did not transform, may be at anambient temperature. For example, the average or mean temperature of theremainder may be an ambient temperature.

In some embodiments, the 3D printing comprises at least one 3D printingmethodology. In some embodiments, the 3D printing comprises a pluralityof different 3D printing methodologies. In some embodiments, the 3Dprinting comprises a plurality of 3D object portions, at least two ofwhich are formed by different 3D printing methodologies. The 3D printingmethodology may depend on the type of portion primed. For example, the3D printing methodology may depend on the geometry of the 3D portion.For example, the 3D printing methodology may depend on the position ofthe 3D portion (e.g., with respect to the platform and/or requested 3Dportion). The at least one 3D object portion (e.g., that ischaracteristic of a 3D printing methodology) comprises forming a (i)porous matrix using a transforming energy beam, (ii) anchorlesslysuspended (e.g., floating) bottom skin layer, (iii) rigid-portion (iv)multi transformation overhang, (v) single-transformation overhang, (vi)thickened overhang, or (vii) high aspect ratio melt pool. A high aspectratio of a melt pool (e.g., FIG. 25A, 2510) may be described as a ratioof a depth of the melt pool (e.g., 2510 “h”) over a radius of theexposed surface of the melt pool (e.g., 2510 “r”). A high aspect ratioof a melt pool (e.g., FIG. 25A, 2510) may be described as a ratio of adepth of the melt pool (e.g., 2510 “h”) over a width of the exposedsurface of the melt pool (e.g., d₃ of 2520). High aspect ratio may bedescribed as a ratio of at least about 1.5. High aspect ratio may be atleast about 1.5, 1.7, 2.0, 2.2, 2.4. 2.5, 2.7, 3.0, 3.2, 3.5, 3.7, 4.0,4.2. 4.5. 4.7, 5.0, 5.5, 6.0, 6.5, 7.0, 7.5, 8.0, 8.5, 9.0, 9.5. or10.0. High aspect ratio may be in any range between the afore-mentionedvalues (e.g., from about 1.5 to about 10.0, from about 1.5 to about 3.0,from about 3.0 to about 4.0, from about 4.0 to about 5.0, from about 3.0to about 8.0, or from about 5.0 to about 10.0). The different optional3D printing methodologies are described in detail herein. The 3Dprinting methodology may comprise (a) directly transforming apre-transformed material into a transformed material, or (b)re-transforming a first transformed material (e.g., that forms ahardened material directly or indirectly) into a second transformedmaterial. The second transformed material may be denser than the firsttransformed material. The second transformed material may have at leastone different microstructure than the first transformed material. Thesecond transformed material may have a different distribution ofmicrostructures as compared to the first transformed material. Thesecond transformed material may have a different number of melt pools ascompared to the first transformed material. The first transformedmaterial may have a first melt pool of a different fundamental lengthscale (abbreviated as “FLS”) (e.g., aspect ratio of its radius to itsdepth) as compared to the second melt pool of the second transformedmaterial. The first transformed material may be more porous than thesecond transformed material. The 3D priming methodology may comprisedensifying a transformed (e.g., porous) structure (e.g., byre-transforming the transformed structure).

In some embodiments, a 3D object portion is generated by forming a hard(e.g., solid) material that is porous. The porous material is referredto herein as a “porous matrix” (abbreviated as “PMX”). The 3D object maybe generated by (i) providing a pre-transformed material to a targetsurface; (ii) transforming at least a portion of the pre-transformedmaterial into a transformed material. The transformation may includeusing a transforming energy beam, such as a laser beam, an electronbeam, and/or other suitable type of energy beam. The transformation maycomprise fusing. The fusing may comprise sintering or melting (e.g.,completely melting). The transformed material may (e.g., subsequently)form a hard (e.g., solid) material that is porous (e.g., a porousmatrix). The pre-transformed material may be provided by streaming it to(e.g., towards) a target surface. The transformation may be at thetarget surface, or adjacent (e.g., directly adjacent) to the targetsurface. The 3D object may be generated by providing a first layer ofpre-transformed material (e.g., powder) in an enclosure; transforming(e.g., hardening) at least a portion of the pre-transformed material toform a first porous matrix layer (e.g., a partially densified layer).The transforming may be effectuated (e.g., conducted) with the aid of atransforming energy beam. The energy beam may travel along a path. Theporous matrix layer may be formed anchorlessly within the enclosure. ThePMX layer may be anchored to the platform. For example, the PMX layermay be formed directly on the platform. For example, the PMX layer maybe anchored using one or more auxiliary support to the platform. Themethod may further comprise forming a second porous matrix layer (e.g.,directly) above the first PMX layer. The second PMX layer may contactthe first PMX layer at one or more positions. A 3D structure comprisinga plurality of porous matrix layers may be referred to herein as a“porous matrix structure” (also herein “PMX structure”). In a PMXstructure, at least a first PMX layer and a second PMX layer(s) may havedifferent porosity percentages (e.g., calculated as volume per volumepercentages, or as area per area percentage). In a PMX structure, atleast a first PMX layer and a second PMX layer(s) may have (e.g.,substantially) porosity percentages (e.g., volume per volume percentagesor as area per area percentage). In a PMX structure, at least a firstPMX layer and a second PMX layer(s) may have (e.g., substantially)identical pore structures (e.g., geometries). In a PMX structure, atleast a first PMX layer and a second PMX layer(s) may have (e.g.,substantially) different pore structures. At times, the PMX layer may besupplemented with pre-transformed material before its re-transformationand/or densification (e.g., by the transforming energy beam). At times,the PMX layer may not be supplemented with pre-transformed materialbefore its re-transformation and/or densification. The method mayfurther comprise transforming the PMX structure to form a hard materialas part of the 3D object. The method may further comprise transformingthe PMX structure to form a denser material as compared to the PMXstructure. The denser (hard) material can be again transformed by athird transformation operation to form an even denser (hard) material.The transformation operations on the porous matrix may repeat until adesired and/or requested density of the hard material is obtained. Hardmay comprise solid. Transforming may comprise re-transforming (e.g.,re-sintering and/or re-melting (e.g., complete re-melting)) the one ormore porous layers. Transforming may comprise forming one or more meltpools within the (e.g., entire) porous matrix. The method may furthercomprise providing a PMX on the previously transformed layers andre-transforming the PMX along with one or more transformed materiallayers. The PMX printing methodology may be used in forming a porousmatrix (“PMX”) structure, multi-transformation overhang, anchorlesslysuspended bottom skin, and a rigid structure. The PMX 3D printingmethodology may comprise forming one or more PMX layers by transforminga pre-transformed material, and subsequently densifying the one or morePMX layers to form respective denser one or more layers. For example, aporous layer may have a porosity of at most about 30%, 40%, 50%, 60%,70%, 70%, or 80% (volume/volume, or area/area porosity relating to anarea of a cross-section plane of maximum porosity). For example, aporous layer may have a porosity of at least about 20%, 30%, 40%, 50%,60%, 70%, or 70%. The porous layer may have a porosity of any valuebetween the afore-mentioned values (e.g from about 20% to about 80%,from about 20% to about 60%, from about 50% to about 80%, or from about30% to about 60%). The PMX 3D printing methodology may use the type-1energy beam (also referred to herein as “hatching energy beam”) and/ortype-2 energy beam (also referred to herein as “tiling energy beam”), asdescribed herein. In some embodiments, the formation of the PMX and itsdensification are performed using the same (e.g., type of) energy beam.In some embodiments, the formation of the PMX is performed using adifferent (e.g., types of) energy beam as the one used for itsdensification.

In some cases, a porosity of a 3D object (or a porosity of portion of a3D object) is determined. In some embodiments, the porosity isdetermined by imaging the object (or a portion of the object) using animaging instrument. In some cases, the imaging instrument uses X-ray(e.g., X-ray photography). In some cases, the imaging instrumentcomprises an optical microscope, scanning electron microscope and/ortunneling electron microscope. In some embodiments, one or more sections(e.g., cross-sections) of the object (or a portion of the object) areimaged. The image(s) can be used to identify pores (e.g., voids) in theobject and/or on a surface of the object. A porosity (or density) can bedetermined by measuring (e.g., and/or estimating) a relative volume ofthe pores compared to a fully dense solid material (e.g., metal). Theporosity can be quantified manually or automatically (e.g., using aprocessor such as a computer). In some embodiments, the porosity isdetermined as a percentage by a volume per volume basis (e.g., volume ofpores versus volume of fully dense solid material). In some embodiments,the porosity is determined as a percentage by an area basis (e.g., areaof pores versus area of fully dense solid material). In someembodiments, the porosity is determined in certain regions of an object.For example, in some case, the porosity of a skin portion of the objectis determined. In some cases, the area porosity is determined along across-section plane. FIG. 39B shows an example cross-section view of a3D object 3950 having a skin portion 5954 and an interior portion (core)3952. In some embodiments, the transformation process(es) for forming askin portion causes formation of a partially dense material thatincludes one or more pores (e.g., 3957). For example, a firsttransformation operation of a MTO process may cause pores to form withina skin. For example, the operation of a STO process may cause pores toform within a skin. In some cases, a melt pool (e.g., of a tile) mayinclude a pore. The interior portion may have a plurality of layers,each of which has a height (e.g., layer thickness). In some cases, thepores are formed deep within the skin portion (e.g., at least about 2,3, 4, 5, 6, or 7 average layer thicknesses from the top of the skin(e.g., skin boundary 3955)) during the printing. In some cases, thepores are formed deep within the melt pool (e.g., at least about 2, 3,4, 5, 6, or 7 average layer thicknesses from the top of the melt pool)during the printing. The depth of the pores can be attributed to byremelting of at least one or more previously hardened layers ofmaterial. For example, the pores can be formed at least about 100micrometers (μm), 200 μm, 300 μm, 400 μm, 500 μm or 1000 μm below atarget surface during printing. In some embodiments, a portion (e.g., amajority (e.g., greater than about 50%)) of the pores in the skinportion are situated closer to the exterior surface of the 3D objectportion (e.g., of a skin) than a boundary (e.g., 3955) between theinterior and skin portions. In some cases, a portion (e.g., a majority(e.g., greater than about 50%)) of the pores are formed below a midline3951) (e.g., in an outermost half thickness) of the skin portion, e.g.,and towards an external bottom surface of the skin. In some embodiments,the interior portion (e.g., 3052) does not border to the portioncomprising the pores at its top boundary layer (e.g., in a ledge portionthat is made up of skin, e.g., FIG. 9, 922). In some embodiments, aportion (e.g., a majority (e.g., greater than about 50%)) of the poresin the skin portion are arranged in a plane (e.g., 3958) that is (e.g.,substantially) parallel to at least a portion of the exterior surface.In some embodiments, an area porosity of the cross-section plane (e.g.,3958) can correspond to a maximum area porosity of the skin portion.FIG. 39C shows an example cross-section view of a 3D object 3960 havinga skin portion 5964 and an interior portion (core) 3962. The exteriorsurface (e.g., 3966) of the object (e.g., skin portion) can include aseries of peaks and valleys. The series of peaks and valleys maycorrespond to the outer surfaces of tiles (e.g., overlapping tiles).Pores (e.g., 3967) within the skin portion may be aligned with across-section plane (e.g., 3968) that is (e.g., substantially) parallelto the exterior surface (e.g., 3966). In some cases, at least one (e.g.,each) melt pool may include a pore. In some embodiments, some (e.g., amajority (e.g., greater than about 50%)) of the pores in the skinportion are situated closer to the exterior surface than a boundary(e.g., 3965) between the interior and skin portions. The melt pool maybe asymmetric, e.g., having a narrower and/or curved bottom portion. Insome cases, a portion (e.g., a majority (e.g., greater than about 50%))of the pores are formed below a midline (e.g., 3961) (e.g., in anoutermost half thickness) of the skin portion, e.g., towards the bottomof the melt pool(s). In some embodiments, an area porosity of thecross-section plane (e.g., 3968) can correspond to a cross section ofthe skin portion having maximum area porosity. In some embodiments, theporosity in the skin portion can be reduced (e.g., (substantially)eliminated) using one or more retransformation operations describedherein. For example, in some embodiments, a second transformationoperation of a MTO process reduces the porosity of the skin portion to atarget porosity. For example, in some embodiments, a secondtransformation operation using the HARMP process reduces the porosity ofthe skin portion to a target porosity.

In some embodiments, the 3D object is devoid of a sacrificial PMX that(e.g., completely) engulfs and/or supports at least a portion of a 3Dobject, wherein the sacrificial PMX is not part of the requested 3Dobject. The PMX may reduce the deformation and/or deformability of theat least a portion of a 3D object. The PMX may support at least aportion of the 3D object from 1, 2, 3, 4, 5, or 6 spatial directions.The PMX may engulf and/or support at least a portion of a 3D object. ThePMX may (e.g., entirely, or substantially entirely) be incorporatedwithin the 3D object upon the completion of the 3D printing.

In some embodiments, the transforming energy beam utilized in formingthe PMX layer (e.g., in its optional re-transformation) travels along apath. The path may comprise hatches. The path may comprise tiles. Ahatch may be formed using a (e.g., constantly) moving energy beam. Theenergy beam may comprise a continuous or discontinuous (e.g., pulsing)energy beam. The energy beam may be any energy beam described herein(e.g., type-1 and/or type-2 energy beam).

In some embodiments, the energy beam forms a tile while irradiating atarget surface. A tile may be formed using a (e.g., substantially)stationary energy beam, for example, to form a tile having a (e.g.,substantially) circular cross section. FIG. 39 shows an example of atile having circumference 3925 formed by an energy beam that irradiatesa portion of a target surface, which energy beam footprint (alsoreferred to herein as an irradiation spot) centers on position 3921during formation of the tile. Substantially stationary may be relativeto the speed and/or propagation direction of the transforming energybeam along the path. For example, a substantially stationary energy beammay move slightly (e.g., oscillate, move back and forth, or dither). Thelength of the movement may be less than a FLS of a footprint of theenergy beam (e.g., around a point). The movement can be with respect to(e.g., around) a point. The point may correspond to a center of theenergy beam or center of the footprint of the energy beam on the targetsurface. The movement may not include a spatial (e.g., lateral) movementgreater than a diameter of the energy beam (e.g., cross section and/orfootprint on the target surface). FIG. 39 shows an example of a tilehaving a circumference resembling oval 3935, formed by an energy beamthat irradiates a portion of a target surface, which energy beamfootprint centers on linear path 3931 and moves in a back and forthmovement along path 3931 during formation of the tile; circumference3937 shows an example of the energy beam circumference when the energybeam is centered in the middle of path 3931. The manner of tileformation may cause different temperature gradient profile along thehorizontal cross section of the tile. For example, when a tile is formedby one spot irradiation using a gaussian beam, the center of the tilemay be hotter than its edges. A tile may be formed using an energy beamthat propagates along a circling or spiraling path, for example, to forma tile having a (e.g., substantially) circular cross section. FIG. 39shows an example of a tile having circumference 3926 formed by an energybeam that irradiates a portion of a target surface, which energy beamfootprint centers on an internal circular path having an arch 3922, andmoves along the circular path during formation of the tile. During itsformation, the center of the tile 3926 may be hotter than an are closeto a circumference 3924 of tile 3926. FIG. 39 shows an example of a tilehaving circumference 3927 formed by an energy beam that irradiates aportion of a target surface, which energy beam footprint centers on aspiraling path that begins in position 3923 and ends in position 3929,and moves along the spiraling path during formation of the tile. In thatmanner, the center of the tile 3927 in position 3929 may be hotter thanthe circumference of the tile 3927, during its formation. A tile may beformed using a slow-moving energy beam (e.g., moving in slow speed), forexample, to form a tile having a horizontally elongated cross section(e.g., that is different from a horizontally circular cross-sectionaltile). At times, the energy beam moves along the path of time duringtile formation along the path-of-tiles at a slow speed. The slow speedmay be of at most about 5000 micrometers per second (pints), 1000 μm/s,500 μm/s, 250 μm/s, 100 μm/s, 50 μm/s, 25 μm/s, 10 μm/s, or 5 μm/s. Theslow speed may be of any value between the afore-mentioned values (e.g.,from about 5000 μm/s to about 5 μm/s, from about 5000 μm/s to about 100μm/s, or from about 500 μm/s to about 5 μm/s. FIG. 39 shows an exampleof a tile having a circumference resembling oval 3936 formed by anenergy beam that irradiates a portion of a target surface, which energybeam footprint centers on line 3932 and moves in a direction along line3932 during formation of the tile; circumference 3934 shows an exampleof the energy beam circumference at the center of line 3931. Themovement of the energy beam (e.g., along the circular, dithering, slowmoving, or spiraling path) may be during a dwell time on the targetsurface (e.g., during a period of melt pool formation) to form the tile.

In some embodiments, a movement of the energy beam may be during a dwelltime on the target surface to form the tile or a hatch. The dwell timemay result in transformation of a target surface (e.g., pre-transformedmaterial), for example, during tile formation and/or during hatching.The path may comprise a vector or a raster path. The method may furthercomprise hardening the transformed material to form a hard material aspart of the 3D object. In some embodiments, the transformed material maybe the hard (e.g., solid) material as part of the 3D object.

In some embodiments, successively formed melt pools (e.g., tiles) areformed using a tiling or hatching methodology using an energy beamconfigured to transform at least a portion of the target surface (e.g.,the irradiated portion of the target surface). The energy beam may be apulsing energy beam or a continuous energy beam. The tiling methodologymay employ a type-2 energy beam (or at times, a type-1 energy beam) asdisclosed herein. The hatching methodology may employ a type-1 energybeam (or at times, a type-2 energy beam) as disclosed herein. In someembodiments of the hatching methodology, the energy beam (e.g., apulsing, or a continuous wave) can be continuously moving along a path(e.g., to form a hatch). When a pulsing energy is used, the distancebetween the formed melt pools may relate to the relative speed of theenergy beam along a path. A melt pool may be formed during a pulse ofthe pulsing energy beam. For example, when the pulsing frequency isconstant, a first distance between formed melt pools is larger whentheir forming energy beam speed is high (e.g., when progressing on astraight path portion), relative to a second distance between formedmelt pools that is smaller when their forming energy beam speed is low(e.g., when progressing on a curved or winding path), which formingenergy beam of the melt pools is the same forming energy beam.

In some embodiments of the tiling methodology, the energy beam movesalong the path intermittently (e.g., in a stop and repeat mode). In someembodiments of the tiling methodology, the distance between tiles (e.g.,melt pools forming the tiles) remains the same, e.g., regardless of thepath section geometry (e.g., straight line, curved, and/or windingpath). In some embodiments of the tiling methodology, the speed of theenergy beam along the path (e.g., which energy movement comprises adwell time and an intermission time) remains the same, e.g., regardlessof the path section geometry (e.g., straight line, curved, and/orwinding path). In some embodiments of the tiling methodology, the energybeam (i) irradiates a portion along a path (e.g., while beingstationary, substantially stationary, or slow moving) with an energydensity (profile) sufficient to transform the material included in theportion (e.g., to form a melt pool), (ii) reduce the power density ofthe energy beam along the path such that no transformation occurs alongthe path, and (iii) repeats steps (i) and (ii) until the path iscompleted. Operation (i) is designated herein as “dwell time” along thepath. Operation (ii) is designated herein as “intermission time” alongthe path. During the intermission time, the power density can be zero,or substantially zero. During the intermission-time the power densitymay be sufficient to heat and not transform the material along the path.During the intermission time, the energy beam may travel elsewhere andirradiate (e.g., heat and/or transform) portions that are outside of thepath (e.g., along a different path). The energy beam may form aplurality of paths in parallel, e.g., by irradiating a first portionduring a first dwell time along a first path while ceasing itsirradiation of a second path (during a first intermission); followed byirradiating a second portion during a second dwell time along a secondpath while ceasing the irradiation of a first path (during a secondintermission). A pulse and/or intermission of the transforming energybeam during a tile formation along the path of tiles may last at leastabout 0.1 milliseconds (msec), 0.5 ms, 1 ms, 5 ms, 10 msc, 30 msec, 50msec, 100 msec, 500 msec, or 1000 msec. A pulse and/or intermission ofthe transforming energy beam during a tile formation may last at most0.5 ms, 1 ms, 5 ms, 10 msc, 30 msec, 50 msec, 100 msec, 500 msec, or1000 msec. A pulse and/or intermission of the transforming energy beamduring a tile formation along the path of tiles may any time spanbetween the afore-mentioned time values (e.g., from about 0.1 msec toabout 1000 msec, from about 0.5 msec to about 50 msec, from about 30msec to about 500 msec, or from about 100 msec to about 1000 msec).

In some embodiments, the 3D object portion comprises an anchorlesslysuspended bottom skin layer (abbreviated herein as “ASBS” layer). TheASBS layer formation methodology may comprise (i) forming one PMX layerand (ii) densifying the PMX layer into a denser layer. In someembodiments, operations (i) and (ii) are performed using the same (e.g.,type of) energy beam. In some embodiments, operations (i) and (ii) areperformed using different (e.g., types of) energy beams. The ASBS layerformation methodology may further comprise densifying the denser layerat least once (e.g., as described herein regarding PMX structuredensification). The PMX layer may be formed by any suitablemethodologies mentioned herein. The ASBS layer formation methodology maycomprise (i) forming one PMX layer and (ii) re-transforming the PMXlayer (e.g., into a denser layer and/or into a layer comprising at leastone different microstructure) to form a transformed PMX layer. The ASBSlayer formation methodology may further comprise re-transforming thetransformed PMX layer at least once (e.g., as described herein regardingPMX structure densification) to form a multi-transformed PMX layer. Theformed layer of the 3D object may be floating anchorlessly within thematerial bed during its formation (e.g., 3D printing). For example, thePMX layer may be suspended anchorlessly in the material bed during itsformation, during its transformation, or any combination thereof. The“bottom skin layer” as used herein comprises the first formed (hard)layer of a 3D object. The ASBS printing methodology may be used to forman anchorlessly floating bottom skin layer of the 3D object, which ASBSanchorlessly floats in the material bed during its 3D printing. Thematerial bed may be devoid of a pressure gradient during the formationof the ASBS. The material bed may be at ambient temperature and/orpressure during the formation of the ASBS. The pre-transformed materialin the material bed may be flowable during the formation of the ASBS.The ASBS may be (e,g substantially) planar. The ASBS may comprise alarge radius of curvature (e.g., as disclosed herein). The height (e.g.,thickness) of the ASBS may be larger than the average height of thesubsequent layer of the 3D object. Larger may be by at least about 1.1times (*), 1.2*, 1.3*, 1.4*, 1.5*, 1.6*, 1.7*, 1.8*, 1.9*, 2.0*, 2.2*,2.5*, 2.8*, 3.0*, 3.2*, 3.4*, 3.5*, 3.8*, 4.0*, 4.2*, 4.4*, 4.6*, 4.8*,or 5.0* thicker than the average height of the succeeding layer of the3D object. Larger may be between any range between the afore-mentionedvalues (e.g., from about 1.1* to about 5.0*, from about 1.2* to about2.0*, from about 2.0* to about 4.0*, or from about 4.0* to about 5.0*)thicker than the average height of the succeeding layer of the 3Dobject.

In some embodiments, the 3D object portion comprises a rigid-portionusing a transforming energy beam. The 3D object can be formed in a 3Dprinting system (e.g., FIG. 1, 100) whereby rigid-portion may beanchored to (e.g., a portion of) the platform, which may include a base(e.g., FIG. 1, 102) anchor a substrate (e.g., FIG. 1, 109), within theenclosure having an atmosphere (e.g., in a volume 126). The platform maycomprise a support surface that supports at least a portion of one ormore 3D objects. The support surface may be a surface of the base (e.g.,102). In some embodiments, the support surface is (e.g., substantially)orthogonal (e.g., normal and/or perpendicular) to the gravitationalfield vector. In some embodiments, the one or more 3D objects areprinted directly on the support surface of the platform (e.g., directlyon the base). The base may also be referred to herein as the buildplate. The enclosure and/or platform may comprise an elemental metal,metal alloy, ceramic, or an allotrope of elemental carbon. The enclosurewall may comprise a non-transparent (e.g., opaque) material. The rigidportion may not yield (e.g., not substantially, e g not detectablyyield), for example, to a force exerted upon by depositing an additional(e.g., layer of) transformed material on the rigid-portion. The rigidportion may not deform (e.g., not substantially or not detectablydeform), for example, upon deposition of an additional (e.g., layer of)transformed material on the rigid portion. The rigid portion may notform one or more defects (e.g., not substantially or not detectably formdefects), for example, upon deposition of an additional (e.g., layer of)transformed material on the rigid portion. Substantially may be relativeto the intended purpose of the 3D object. In some embodiments, therigid-portion may be thick enough to resist stress (e.g., upondepositing an additional (e.g., layer of) transformed material on therigid-portion). The rigid portion may be thick enough to resistdeformation (e.g., upon depositing an additional (e.g., layer of)transformed material on the rigid-portion). In some embodiments, therigid-portion may be thick enough to resist formation of defects therein(e.g., upon depositing an additional (e.g., layer of) transformedmaterial on the rigid-portion). The rigid portion may have a thickness(e.g., height or depth, e.g., as shown in FIG. 4) of at least about 0.6millimeters (mm), 0.8 mm, 1.0 mm, 1.1 mm, 1.2 mm, 1.3 mm, 1.4 mm, 1.5mm, 1.6 mm, 1.8 mm, 2.0 mm, 2.2 mm, 2.6 mm, 5.0 mm, 10 mm, 20 mm, 50 mm,or 100 mm. Thickness of the rigid-portion may be in a range between anyof the afore-mentioned values (e.g., from about 1.0 mm to about 100 mm,from about 0.6 mm to about 2.6 mm, from about 0.8 mm to about 2.0 m,from about 1 mm, to about 1.8 mm, from about 1.2 mm to about 1.6 mm,from about 1.2 mm to about 5.0 mm, from about 5.0 mm to about 20 mm, orfrom about 20 mm to about 100 mm). The rigid-portion may provide supportfor formation of an additional portion of the 3D object (e.g., anoverhang structure). The rigid-portion may be a part of the forming 3Dobject.

In some embodiments, the rigid portion does not respond to stressdeformation on adding a transformed material (e.g., layer of transformedmaterial) thereon. The rigid-portion may comprise shallow melt pools.The rigid-portion may have a (e.g., substantially) homogeneously sized(e.g., hemispherical) melt pools. The shallow to hemispherical meltpools may have an aspect ratio (e.g., depth of the melt pool to theradius of the exposed surface of the melt pool) of at most about 0.01,0.05, 0.1, 0.2, 0.3, 0.4, 0.5, 0.75, 1, 1.2, 1.3, or 1.4, The shallow tohemispherical inch pools may have an aspect ratio of the depth of themelt pool to the radius of the exposed surface of the melt pool, of anyvalue between the afore-mentioned values (e.g., from about 0.01 to about1.4, from about 0.01 to about 0.75, or from about 0.75 to about 1.4).The rigid-portion may be formed using a transforming energy beam (e.g.,type-2 energy beam or type-1 energy beam).

In some embodiments, at least one layer of the rigid portion is formedby (e.g., a repetition of) a single transformation procedure oroperation (abbreviated as “STO)”). The single transformation proceduremay comprise (i) depositing a pre-transformed material on a targetsurface (e.g., a platform or an exposed surface of a material bed), and(ii) using a transforming energy beam to transform the pre-transformedmaterial to form a transformed material that forms at least a part ofthe 3D object. Operations (i) to (ii) may be repeated until a desired 3Dshape and/or FLS of the rigid portion is reached. The transformingenergy beam may follow a path to form a layer of transformed material.The pre-transformed material may be deposited to the target surfacelayerwise (e.g., layerwise deposition of particulate material such aspowder). The layerwise deposition may comprise depositing planar layersof pre-transformed material (e.g., of a predetermined height). Thepre-transformed material may be deposited towards the target surface ina stream of pre-transformed material, and is transformed by thetransforming energy beam at or closely adjacent to, the target surface(e.g., direct material deposition).

The rigid-portion may be generated by layerwise deposition. Thelayerwise deposition may comprise providing a first layer ofpre-transformed material as part of a material bed (e.g., FIG. 1, 104)in an enclosure above a platform; and transforming at least a portion ofthe pre-transformed material to form a transformed material as part ofthe rigid-portion. The transformation may be effectuated (e.g.,conducted) with the aid of a transforming energy beam (e.g., a type-1energy beam (e.g., 101) or a type-2 energy beam (e.g., 108)). Thetransforming energy beam(s) may travel along a path. The method mayfurther comprise providing a second layer of pre-transformed materialadjacent to (e.g., above) the first layer, and repeating thetransformation process (e.g., as delineated herein), to form at least apiece of the rigid-portion. Repeating operation (i) to provide asubsequent layer of pre-transformed material above the layer oftransformed material and (ii) transforming (e.g., hardening) thepre-transformed material in the subsequent layer. The repetition may bedone at least until the rigid-portion reaches a thickness that wouldallow it not to respond to a stress deformation upon adding, atransformed material.

In some embodiments, at least one layer of the rigid portion may beformed by multiple transformation. The multiple transformation may be ofat least a portion of the material bed. The multiple transformation maycomprise forming a PMX layer (e.g., as described herein). The PMX layermay be formed using a first transformation operation in whichpre-transformed material is transformed into a (porous) firsttransformed material (that is hard or that hardens). The poroustransformed material may form a hard (e.g., solid) porous material thatis referred to herein as a “PMX material.” The PMX may be (e.g.,subsequently) supplemented with pre-transformed material, or notsupplemented with pre-transformed material prior to a secondtransformation operation. In the second transformation, at least aportion of the PMX may be re-transformed into a second transformedmaterial that forms a denser hard material as compared to the PMX. Thedenser hard material can be transformed again by a third transformationoperation to form an even denser hard material. The transformationoperations on the PMX may repeat until a desired and/or requesteddensity of the hard material is obtained.

In some embodiments, the 3D object portion is generated using amulti-transformation process or operation (abbreviated as “MTO” process)to form an overhang. The overhang may be a 3D plane (e.g., that isconnected it at least one, two, or three direction to a rigid portion(e.g., core) structure. The overhang may comprise a shelf, or a blade.The overhang may comprise (e.g., correspond to) a ceiling of a cavity(e.g., that is connected to the core at all its sides) or a bottom of acavity. The 3D object portion may be generated by (i) providing a firstlayer of pre-transformed material that is adjacent to (e.g., above) arigid-portion, within an enclosure (e.g., in a material bed); (ii)forming a first PMX layer from at least a portion of the first layer ofthe pre-transformed material; and (iii) transforming the PMX layer toform a first dense layer (e,g, that is denser than the first. PMXlayer). The MTO process may be used to form the first formed layer ofthe overhang. For example, the MTO process may be used to form thebottom skin of the overhang structure. The MTO process may be used toform the bottom skin of at least a portion of an overhang (e.g., cavityceiling or bottom). The MTO method may further comprise repeatingoperations (i) to (iii). For example, by (iv) providing a second layerof pre-transformed material that is adjacent to (e.g., above) the firstdense layer; (v) forming a second PMX layer from at least a portion ofthe second layer of pre-transformed material, which second PMX layerpartially overlaps or contacts the first dense layer; and (vi)transforming the second PMX layer to form a second dense layer (e.g.,that is denser than the second PMX layer). The first dense structure mayconnect (e.g., weld) to the rigid-portion in at least one position(e.g., and otherwise be devoid of an auxiliary support). The seconddense structure may connect (e.g., weld) to the first dense structure inat least one position (e.g., and otherwise be devoid of auxiliarysupport). The non-overlapping portion of the second dense structure mayextend in the direction away from the rigid-portion (e.g., in thedirection towards the overhang extension). The overhang may form anangle with respect to the rigid portion and/or platform. The MTOmethodology maybe used to form an overhang having an angle with respectto a direction parallel to the platform, or with a directionperpendicular to the platform. In some embodiments, the MTO methodologymay be used to form an overhang with a shallow angle. The angle may beshallow to a prescribed degree. Shallow may be an angle of at most about40°, 35°, 30°, 25°, 20°, 15°, 10°, 8°, 5°, 4°, 3°, 2°, 1°, 0.5° or 0°,with respect to a direction parallel to the platform. Shallow may be anyangle between the afore-mentioned angles, with respect to a directionparallel to the platform (e.g., from about 0° to about 40°, from about30° to 0°, from about 20° to 0°, from about 10° to 0°, or from about 5°to 0°). In some embodiments, the MTO methodology may be used to form anoverhang with a steep angle (e.g., above 40 degrees with respect to adirection parallel to the platform). Steep may be an angle of at mostabout 50°, 40°, 35°, 30°, 25°, 20°, 15°, 10°, 8°, 5°, 4°, 3°, 2°, 1°,0.5° or 0°, with respect to a direction perpendicular to the platform.Steep may be any angle between the afore-mentioned angles, with respectto a direction perpendicular to the platform (e.g., from about 0 toabout 40°, from about 30° to 0°, from about 20° to 0°, from about 10° to0°, or from about 5° to 0°). In some embodiments, the MTO methodologymay be used to form an overhang with an obtuse angle (e.g., above 90degrees with respect to a direction perpendicular to the platform).Obtuse may be an angle of at least about 91°, 100°, 110°, 120°, 130°,140°, 150°, 160°, 170°, or 179° with respect to direction perpendicularto the platform. Obtuse may be any angle between the afore-mentionedangles, with respect to a direction perpendicular to the platform (e.g.,from about 91° to about 179°, from about 91° to 120°, from about 120° to150°, from about 150° to 179°, or from about 100° to 179°). The MTOprinting methodology may be used for forming a (e.g., complex) portionof a 3D object (e.g., a shallow angled structure or a wedge). Thetransformation may be done using the transforming energy beam (e.g., thetype-2 energy beam). In some embodiments, at least two of the operations(ii)-(iii) and (v)-(vi) are performed using the same e.g., type of)energy beam. In some embodiments, at least two of the operations(ii)-(iii) and (v)-(vi) are performed using different (e.g., types of)energy beams (at least two of the operations comprises all theoperations delineated).

In some embodiments, a PMX layer is used (e.g., directly) to support arigid structure. For example, the 3D object portion may be generated by(i) providing a first layer of pre-transformed material in an enclosure(e.g., in a material bed); (ii) forming a PMX layer from at least aportion of the first layer of the pre-transformed material; (iii)depositing a second layer of pre-transformed material that is adjacentto (e.g., above) the first PMX layer; and (iv) forming a rigid-portionon the first layer. The PMX layer may be sufficient to support therigid-portion, for example, when the requested rigid portion is small,when the PMX layer is small, or any combination thereof. In someembodiments, a sufficiently small rigid portion has a FLS (e.g., lengthand/or width) of at most about 20 millimeters (mm), 15 mm, 10 mm, 5 mm,4 mm, 3 mm, 2 mm or 1 mm. A sufficiently small rigid portion can have aFLS between any of the afore-mentioned values (e.g., from about 1 mm toabout 20 mm, from about 1 mm to about 10 mm, or from about 10 mm toabout 20 mm). In some embodiments, a sufficiently small rigid portionhas a radius of curvature of at least about 35 mm, 30 mm, 25 mm 20 mm,15 mm, 10 mm, 5 mm or 1 mm. A sufficiently small rigid portion can havea radius of curvature mentioned herein.

In some embodiments, the 3D object is generated using a singletransformation process (abbreviated as “STO” process) to form anoverhang. The 3D object may be generated by (i) providing a first layerof pre-transformed material (e.g., to form a material bed) in anenclosure above a platform, which material bed comprises arigid-portion; and (ii) transforming at least a portion of thepre-transformed material to form a first layer of transformed material(e.g., that subsequently hardens into a hard material), whichtransformed material contacts and/or overlaps the rigid-portion. Thetransforming may be effectuated with the aid of a transforming energybeam (e.g., the type-2 energy beam). The energy beam may travel along apath. The STO printing methodology may be used for forming a (e.g.,complex) portion of a 3D object (e.g., an overhang structure, a bottomskin layer, an (e.g., shallow) angled structure, or a wedge). The methodmay further comprise repeating operations (i) and (ii). For example, themethod may further comprise (iii) dispensing a second layer ofpre-transformed material above the first transformed material, and (iv)transforming at least a portion of the second pre-transformed layer toform a second layer of transformed material as part of an overhangstructure that is a portion of the 3D object. The STO process may beused to form the first formed layer of the overhang. For example, theSTO process may be used to form the bottom skin of the overhangstructure. The STO process may be used to form the bottom skin of atleast a portion of an overhang (e.g., cavity ceiling or bottom). Thefirst may connect (e.g., weld) to the rigid-portion in at least oneposition (e.g., and otherwise be devoid of auxiliary support). Thesecond layer of transformed material may connect (e.g., weld) to thefirst layer of transformed material in at least one position (e.g., andotherwise be devoid of auxiliary support). The non-overlapping portionof the second layer of transformed material may extend in the directionaway from the rigid-portion (e.g., in the direction towards the overhangextension). The overhang may form an angle with respect to the rigidstructure and/or platform. The STO methodology may be used to form anoverhang having an angle with respect to a direction parallel to theplatform, or with a direction perpendicular to the platform. In someembodiments, the STO methodology may be used to form an overhang with ashallow angle. The angle may be shallow to a prescribed degree. Shallowmay be an angle of at most about 40°, 35°, 30°, 25°, 20°, 15°, 10°, 8°,5°, 4°, 3°, 2°, 1°, 0.5° or 0°, with respect to a direction parallel tothe platform. Shallow may be any angle between the afore-mentionedangles, with respect to a direction parallel to the platform (e.g., fromabout 0° to about 40°, from about 30° to 0°, from about 20° to 0°, fromabout 10° to 0°, or from about 5° to 0°. In some embodiments, the STOmethodology may be used to form an overhang with a steep angle (e.g.,above 40 degrees with respect to a direction parallel to the platform).Steep may be an angle of at most about 50°, 40°, 35°, 30°, 25°, 20°,15°, 10°, 8°, 5°, 4°, 3°, 2°, 1°, 0.5° or 0°, with respect to adirection perpendicular to the platform. Steep may be any angle betweenthe afore-mentioned angles, with respect to a direction perpendicular tothe platform (e.g., from about 0° to about 40°, from about 30° to 0°,from about 20° to 0°, from about 10° to 0°, or from about 5° to 0°). Insome embodiments, the STO methodology may be used to form an overhangwith an obtuse angle (e.g., above 90 degrees with respect to a directionperpendicular to the platform). Obtuse may be an angle of at least about91°, 100°, 110°, 120°, 130°, 140°, 150°, 160°, 170°, or 179° withrespect to a direction perpendicular to the platform. Obtuse may be anyangle between the afore-mentioned angles, with respect to a directionperpendicular to the platform (e.g., from about 91° to about 179°, fromabout 91° to 120°, from about 120° to 150°, from about 150° to 179°, orfrom about 100° to 179°). The transformation may be done using thetransforming energy beam (e.g., the type-2 energy beam). In someembodiments, operations (ii) and (iv) are performed using the same(e.g., type of) energy beam. In some embodiments, operations (ii) and(iv) are performed using different (e.g., types of) energy beams.

In some embodiments, the 3D object is generated using an STO processand/or an MTO process in combination with a porous matrix (PMX)structure, to form a thickened overhang. The 3D object may be generatedby (i) providing a first layer of pre-transformed material (e.g., toform a material bed) in an enclosure above a platform, (ii) generating arigid-portion (e.g., that is or is not anchored to the platform), (iii)performing an STO or an MTO process to form a first overhang structurethat is anchored to the rigid portion. The first overhang structure maybe a part of an elongated overhang structure. The first overhangstructure may be elongated in subsequent layers. For example, a secondoverhang structure can be formed by depositing a second layer ofpre-transformed material, performing an STO or MTO process to form asecond overhang structure, wherein the second overhang structure anchors(e.g., connects to) the first overhang structure. The first overhangstructure may partially overlap the second overhang structure. Theoverhang elongation process may be repeated in a plurality of layersuntil the desired overhang skin is formed. To thicken the skin of theoverhang (e.g., which skin is made using the STO or MTO process), aportion of a layer of pre-transformed material disposed above thepreviously formed overhang, is transformed into a porous matrix (PMX).For example, the method may further comprise providing a second layer ofpre-transformed material above the first overhang structure, performingan STO or MTO process to form the second overhang structure, andadjacent second overhang structure, performing an PMX process to form aporous matrix above at least a portion of the first overhang structure,which porous layer connects to the first overhang structure. At least aportion of the first overhang structure may be connected (e.g., in asubsequent layer) with a porous material (e.g., formed by the PMXprocess) to thicken the first overhang structure. The overhang structureand/or the porous matrix may be transformed to form a transformedmaterial as a part of the thickened overhang structure of a forming 3Dobject, which transformed material is denser than the PMX. At times, thethickened overhang structure may not be transformed (e.g.,re-transformed). At times, the overhang structure may be thickened usingthe type-2 energy beam.

In some embodiments, the 3D object portion is generated by forming oneor more high aspect ratio melt pools (abbreviated as HARMP). The HARMPmay be utilized in a tiling or hatching methodology. For example, theHARMP may be formed by a continuously moving energy beam, or by analternatingly moving energy beam (e.g., stop and repeat mode). In someexamples, the HARMP in at least a portion of a layer of hardenedmaterial may be formed by a continuously moving energy beam. The highaspect ratio melt pool may (e.g., substantially) have a parabolicvertical cross section (e.g., with its extremum at the bottom of themelt pool). Aspect ratio may be described as a relation (e.g., a ratio)of a depth (or height) of the melt pool (e.g., FIG. 25A, 2510 “h”) tothe radius of the exposed surface of the melt pool (e.g., 2510 “r”). Theradius of a high aspect ratio melt pool may be shorter (e.g.,substantially) than the depth of the melt pool. For example, for a highaspect ratio melt pool, if the melt pool has a radius “r”, the depth ofthe melt pool may be at least “2r”, forming an aspect ratio of 2.0. Thehigh aspect ratio melt pool may have a narrow, elongated structure(e.g., having an aspect ratio of at least about 1.5, 2.0, 2.5, 3.0, 4.0,4.5 or 5.0) The HARMP process may comprise (i) irradiating a position ofa target surface in a (e.g., substantially) stationary position with atransforming energy beam that is configured to form a high aspect ratiowell comprising the irradiated position, and extending below the targetsurface; (ii) optionally elongating the well laterally (e.g., byextending the amount of transformed (e.g., molten) material) by movingthe transforming energy beam laterally (e.g., horizontally), and (iii)gradually lowering the intensity of the transforming energy beam toallow closure of the formed well to form a melt pool. The graduallowering of the intensity may allow the melt pool to form with adiminished formation of pores. The pores may comprise at most about 20%,15%, 10%, 5%, 2%, 1%, 0.5%, 0.1%, or 0% of the melt pool. The percentagemay be calculated volume per volume, or area per area (e.g., which areais a cross-sectional plane of maximum porosity in the 3D object). Thepores may comprise a percentage of the melt pool that is between any ofthe afore-mentioned values (e.g., from about 20% to about 0%, from about10% to about 0%, from about 5% to about 0%, or from about 2% to about0%). Forming the well may comprise vaporizing the (e.g., transformed)material. Forming the well may comprise irradiating such that the (e.g.,transformed) material may be form plasma. At times, the 3D object maycomprise a complex structure (e.g., a wedge or a small horizontal crosssection area). The transforming energy beam may be a high-power energybeam. The transforming energy beam may be a focused energy beam. Thetransforming energy beam may have a small FLS (e.g., cross section). Thecomplex portion of the 3D object may be formed using the HARMP printingmethodology. Substantially may be relative to the intended purpose ofthe 3D object. Substantially may be relative to the effect on theforming melt pool. Substantially stationary may result in a melt poolthat has a homogenous (e.g, round) horizontal cross section. The targetsurface may comprise a portion of a 3D object. The portion may have beenformed using any 3D printing methodology described herein. The portionmay comprise a fine structure. The target surface may comprise astructure formed by a methodology other than 3D printing (e.g., welding,machining, or sculpting). The target surface may comprise the exposedsurface of a material bed.

In some embodiments, in situ and/or real-time processing is implementedduring a 3D printing operation. A first hardened material may be formedby transforming a pre-transformed material. The first hardened materialmay subsequently be transformed to a second hardened material (e.g., insitu during the 3D printing). For example, an energy beam can be used ina second transformation (e.g., second melting) to transform a hardenedmaterial that was formed by a first transformation (e.g., first melting)of a pre-transformed material (e.g., powder). In some embodiments, theprocess comprises re-transforming a hardened material to control one ormore of its (e.g., material) characteristics. The control may be insitu, and in some cases in real-time during the 3D printing. The in situand/or real-time processing can be implemented by a controller of the 3Dprinting system that is configured to send instructions to the energybeam source (e.g., laser) to perform specified in situ and/or real-timeprocessing operations. The one or more characteristics may comprisesurface roughness or density (or conversely porosity). The secondtransformation can be subsequent (e.g., immediately subsequent) to thefirst transformation. The second transformation of at least a portion ofthe hardened material can follow the first transformation, e.g., withoutan intermediate transformation operation performed on the hardenedmaterial. The second transformation can be used to, for example, alterat least one characteristic of the hardened material formed by the firsttransformation. The hardened material formed by the first transformationmay have a first density. The second transformation can be used, e.g.,(i) to alter the first density of the hardened material to form ahardened material of a second density, and/or (ii) to alter the surfaceroughness of the hardened material after the first transformation. Forexample, the second transformation can be used to increase the firstdensity of the hardened material to form a hardened material of a seconddensity (that is denser than the first density), and/or to reduce thesurface roughness of the hardened material after the firsttransformation. In some embodiments, the first density is at most about30%, 40%, 50% 60%, 70%, 80% or 90% dense (measured as volume by volume,designated herein as “v/v”, or area/area porosity, e.g., of across-sectional plane of maximum porosity). In some embodiments, thesecond density is at least about 85% or 90%, 95%, 98%, 99%, 99.5%, 99.8%dense (v/v, or area/area porosity, e.g., of a cross-sectional plane ofmaximum porosity). The second transformation operation can increase thefirst density of the hardened material by about 110%, 120%, 130%, 140%,150% to form the second density of the hardened material (v/v, area/areaporosity, e.g., of a cross-sectional plane of maximum porosity). Thesecond transformation operation can increase the first density by anypercentage between the afore-mentioned percentages (e.g., from about110% to about 150%, or from about 130% to about 150%). The secondtransformation operation can be controlled to decrease the density ofthe first density of the hardened material. In some embodiments, thesecond transformation operation can reduce a measured roughness of anexposed surface of the hardened material (i.e., smooth the exposedsurface) by; a multiplier (e.g., by at least about 1/2, 1/4, 1/6, 1/8,or 1/10). For example, a measured roughness (e.g., profile roughness Ra,or area roughness Sa) of the exposed surface of the second hardenedmaterial (that underwent the second transformation) can be reduced tohave an Ra er Sa value of at most about 80 μm, 70 μm, 60 μm, 50 μm, 40μm, 30 μm, 20 μm, 10 μm, or 5 μm. The measured roughness of the exposedsurface of the second hardened material can have an Ra value between anyof the afore-mentioned values (e.g., from about 80 μm to about 5 μm,from about 60 μm to about 5 μm, from about 40 μm to about 20 μm, fromabout 30 μm to about 5 μm). In some embodiments, the secondtransformation operation is controlled to increase the surface roughnessof the hardened material after the first transformation,

In some embodiments, during a first transformation and a secondtransformation, the same type of energy beam movement methodology isused, whether tilling methodology or hatching methodology. In someembodiments, during the first transformation and the secondtransformation, a different type of energy beam movement methodology isused. For example, the first transformation can use a tiling movementmethodology (e.g., stop and repeat), and the second transformation canuse a hatching movement methodology (e.g., continuous movement). Thehatching movement methodology may comprise an energy beam thatconstantly moves (e.g., at the same speed) during formation of a path,or during formation of a layer of hardened material.

In some embodiments, during a first transformation and a secondtransformation, the same type of transformation process is used, whethercore. PMX, MTO, STO, or HARMP processes described herein. In someembodiments, during the first transformation and the secondtransformation, a different transformation process is used. For example,the first transformation can use a STO process, and the secondtransformation can use a HARMP process.

The second transformation operation can be any suitable type oftransformation operation described herein. For example, the secondtransformation operation can involve one or more core, PMX, MTO, STO, orHARMP processes described herein. In some cases, the type of secondtransformation process implemented is chosen based on the aspect ratioand/or shape of the melt pools achieved by the second transformationprocess. For example, the second transformation process can involve alow aspect ratio (e.g., shallow), homogeneously dimensioned (e.g.,hemispherical), or high aspect ratio (e.g., deep) melt pools. In someimplementations, a high-aspect-ratio-melt-pool (HARMP) process is usedto transform at least one layer of material that is at least partiallyhardened (e, g., which at least one layer was :formed using one or moreof core, PMX, MTO, STO, or HARMP processes described herein). That is,the second transformation operation can transform the at least onehardened or partially hardened layer of material. For example, thesecond transformation operation can transform a plurality of hardened orpartially hardened layers of material. In some cases, the secondtransformation process can process at most 2, 3, 4, 5, 6, 8, or 10layers of hardened or partially hardened material. In some embodiments,the second transformation process transforms a particular height ofhardened or partially hardened material. For example, in someembodiments the second transformation process transforms a hardened orpartially hardened material having a height of at least about 300 μm,400 μm, 500 μm, 600 μm, 700 μm, 800 μm, 900 μm, or 1000 μm (e.g.,depending on the nature of material and the power density of the energybeam). The second transformation process may transform a hardened orpartially hardened material having a height between any of theabove-mentioned heights (e.g., from about 300 μm to about 1000 μm, fromabout 400 μm to about 800 μm, or from about 500 μm to about 700 μm).

In some embodiments, the 3D object is an extensive 3D object. The 3Dobject can be a large 3D object. The 3D object may comprise a hangingstructure (e.g., wire, ledge, shelf, or 3D plane). In some embodiments,the 3D object includes a geometry that comprises an overhang structureconnected to at least one rigid-portion (also referred herein as “core”)that may be a part of the 3D object. The rigid-portion may providesupport to a second portion (e.g., an overhang structure such as astructure comprising a ledge having a constant or varying angle withrespect to the rigid-portion and/or platform) of the 3D object. Theangle may be acute (e.g., steep, or shallow), or obtuse (e.g., asindicated herein). Examples of such an overhang 3D structure maycomprise an arch, dome, ledge, or blade. For example, the 3D object maycomprise a ledge having a constant or varying angle (e.g., with respectto a platform). FIG. 9 shows an example of an overhang structure (e.g.,922) connected to a rigid-portion (e.g., 920). The overhang structuremay be formed within a material bed. At times, the overhang structuremay be formed on a target surface (e.g., on an exposed surface of thematerial bed, on a platform, or connected to a rigid-portion (e.g., thatis formed on a platform)). The rigid-portion may be connected (e.g.,anchored) to a build plane (also referred to as a build plate) or aplatform (e.g., 915). The overhang (e.g., the hanging ledge stricture)may be printed without auxiliary supports other than the connection tothe one or more rigid-portions (that are part of the requested 3Dobject). The overhang may be formed at an angle (e.g., 930) with respectto the build plane and/or platform (e.g., 915). The overhang and/or therigid-portion may be formed from the same or different pre-transformedmaterial (e.g., powder).

In some embodiments, the 3D object is a large object. In someembodiments, the 3D object is a small object. Small is an object that isnot large. The 3D object may be described as having a fundamental lengthscale of at least about 1 centimeter (cm), 1.5 cm, 2 cm, 10 cm, 20 cm,30 cm, 40 cm, 50 cm, 60 cm, 70 cm, 80 cm, 90 cm, 1 m, 2 m, 3 m, 4 m, 5m, 10 m, 50 m, 80 m, or 100 m. In some instances, the fundamental lengthscale (e.g., the diameter, spherical equivalent diameter, diameter of ahounding circle, or largest of height, width and length; abbreviatedherein as “FLS”) of the printed 3D object can be at least about 50micrometers (μm), 80 μm, 100 μm, 120 μm, 150 μm, 170 μm, 200 μm, 230 μm,250 μm, 270 μm, 300 μm, 400 μm, 500 μm, 600 μm, 700 μm, 800 μm, 1millimeter (mm), 1.5 mm, 2 mm, 5 mm, 1 centimeter (cm), 1.5 cm, 2 cm, 10cm, 20 cm, 30 cm, 40 cm, 50 cm, 60 cm, 70 cm, 80 cm, 90 cm, 1 meter (m),2 m, 3 m, 4 m, 5 m, 10 m, 50 m, 80 m, or 100 m. The FLS of the printed3D object can be at most about 1000 m, 500 m, 100 m, 80 m, 50 in, 10 m,5 m, 4 m, 3 m, 2 m, 1 m, 90 cm, 80 cm, 60 cm, 50 cm, 40 cm, 30 cm, 20cm, 10 cm, or 5 cm. In some cases, the FLS of the printed 3D object maybe in between any of the afore-mentioned FLSs (e.g., from about 50 μm toabout 1000 m, from about 120 μm to about 1000 m, from about 120 μm toabout 10 m, from about 200 μm to about 1 m, from about 1 cm to about 100m, from about 1 cm to about 1 m, from about 1 m to about 100 m, or fromabout 150 μm to about 10 m). The FLS (e.g., horizontal FLS) of the layerof hardened material may have any value listed herein for the FLS of the3D object.

In some embodiments, the material (e.g., pre-transformed material,transformed material, or solid material) comprises an elemental metal,metal alloy, ceramic, or an allotrope of elemental carbon. The allotropeof elemental carbon may comprise amorphous carbon, graphite, graphene,diamond, or fullerene. The fullerene may be selected from the groupconsisting of a spherical, elliptical, linear, and tubular fullerene:The fullerene may comprise a buckyball or a carbon nanotube. The ceramicmaterial may comprise cement. The ceramic material may comprise alumina.The material may comprise sand, glass, or stone. In some embodiments,the material may be devoid of an organic material, for example, apolymer or a resin. In some embodiments, the material may exclude anorganic material (e.g., polymer). At times, the material may comprise anorganic material (e.g., a polymer or a resin). In some embodiments, theterm “particulate material” may be exchanged by a “pre-transformed”material. The pre-transformed material may comprise a particulatematerial. The pre-transformed material may comprise a liquid, solid, orsemi-solid. Pre-transformed material as understood herein is a materialbefore it has been transformed by an energy beam during the 3D printingprocess. The pre-transformed material may be a material that was, or wasnot, transformed prior to its use in the 3D printing process.

At times, the pre-transformed material comprises a particulate material.The particulate material may comprise powder. The pre-transformed (e.g.,powder) material may comprise a solid material. The particulate materialmay comprise one or more particles or clusters. The term “powder,” asused herein, generally refers to a solid having fine particles. The“particulate material” may comprise powder material, or particles madeof another material (e.g., liquid, or semi-liquid containing vesicles).The semi-liquid material may be a gel. The particulate material maycomprise semi-liquid particles. Powders may be granular materials. Thepowder particles may comprise nanoparticles or microparticles. In someexamples, a powder comprising particles having an average FLS (e.g., thediameter, spherical equivalent diameter, diameter of a bounding circle,or the largest of height, width and length; herein designated as “FLS”)of at least about 5 nanometers (run), 10 nm, 20 nm, 30 nm, 40 nm, 50 nm,100 nm, 200 nm, 300 nm, 400 nm, 500 nm, 1 μm, 5 μm, 10 μm, 15 μm, 20 μm,25 μm, 30 μm, 35 μm, 40 μm, 45 μm, 50 μm, 55 μm, 60 μm, 65 μm, 70 μm, 75μm, 80 μm, or 100 μm. The particles comprising the powder may have anaverage FLS of at most about 100 μm, 80 μm, 75 μm, 70 μm, 65 μm, 60 μm,55 μm, 50 μm, 45 μm, 40 μm, 35 μm, 30 μm, 25 μm, 20 μm, 15 μm, 10 μm, 5μm, 1 μm, 500 nm, 400 nm, 300 nm, 200 nm, 100 nm, 50 nm, 40 nm, 30 nm,20 nm, 10 nm, or 5 nm. In some cases, the powder may have an average FLSbetween any of the values of the average particle FLS listed above(e.g., from about 5 nm to about 100 μm, from about 1 μm to about 100 μm,from about 15 μm to about 45 μm, from about 5 μm to about 80 μm, fromabout 20 μm to about 80 μm, or from about 500 nm to about 50 μm).

In some embodiments, at least parts of the layer of pre-transformedmaterial are transformed to a transformed material (e.g., using anenergy beam) that subsequently form at least a fraction (also usedherein “a portion,” or “a part”) of a hardened (e.g., solidified) 3Dobject. At times a layer of transformed and/or hardened material maycomprise a cross section of a 3D object (e.g., a horizontal crosssection). The layer may correspond to a cross section of a requested 3Dobject (e.g., a model). At times a layer of transformed or hardenedmaterial may comprise a deviation from a cross section of a model of a3D object. The deviation may include vertical or horizontal deviation. Apre-transformed material layer (or a portion thereof) can have athickness (e.g., layer height) of at least about 0.1 micrometer (μm),0.5 μm, 1.0 μm, 10 μm, 50 μm, 100 μm, 150 μm, 200 μm, 300 μm, 400 μm,500 μm, 600 μm, 700 μm, 800 μm, 900 μm, or 1000 μm. A pre-transformedmaterial layer (or a portion thereof) can have a thickness of at mostabout 1000 μm, 900 μm, 800 μm, 700 μm, 60 μm, 500 μm, 450 μm, 400 μm,350 μm, 300 μm, 250 μm, 200 μm, 150 μm, 100 μm, 75 μm, 50 μm, 40 μm, 30μm, 20 μm, 10 μm, 5 μm, 1 μm, or 0.5 μm. A pre-transformed materiallayer (or a portion thereof) may have any value in between theafore-mentioned layer thickness values (e.g., from about 1000 μm toabout 0.1 μm, 800 μm to about 1 μm, from about 600 μm to about 20 μm,from about 300 μm to about 30 μm, or from about 1000 μm to about 10 μm).In some embodiments, the FLS (e.g., height or length) of the bottom skinlayer (e.g., the first formed layer of the 3D object) is greater thanthe average or mean FLS of subsequent layers. The layer can be ofparticulate, transformed, and/or hardened material. Greater can be by atleast about 1.25*, 1.5*, 2*, 2.5*, 3*, 3.5*, 4*, 4.5*, 5*, 5.5*, 6*, 7*,8*, 9*, 10* or 11 times (*). Greater can be by at most about 1.25*,1.5*, 2*, 2.5*, 3*, 3.5*, 4*, 4.5*, 5*, 5.5*, 6*, 7*, 8*, 9*, 10* or 11times (*). Greater can be by any value between the afore-mentionedvalues (e.g., from about 1.25* to about 10*, from about 5* to about 11*,or from about 1.25* to about 5*). In some embodiments, a subsequenttransformation (e.g., tiling) operation may cause a portion of thebottom skin to be consumed by (e.g., coalesce with) the subsequentlytransformed material (e.g., tiles). In some cases, this causes the tileto draw in the bottom skin. In some cases, a bottom skin having a FLS(e.g., height or length) of a least a prescribed FLS may assure that thebottom skin is not (e.g., substantially) drawn in by the subsequenttransformed material (e.g., tiles).

In some embodiments, the material composition of at least two of aplurality of layers in the material bed is different. The materialcomposition of at least one layer within the material bed may differfrom the material composition within at least one other layer in thematerial bed. The material composition of at least one layer within the3D object may differ from the material composition within at least oneother layer in the 3D object. The difference (e.g., variation) maycomprise difference in grain (e.g., crystal) structure. The variationmay comprise variation in grain orientation, material density, degree ofcompound segregation to grain boundaries, degree of element segregationto grain boundaries, material phase, metallurgical phase, materialporosity, crystal phase, crystal structure, or material type. Themicrostructure of the printed object may comprise planar structure,cellular structure, columnar dendritic structure, or equiaxed dendriticstructure.

At times, the pre-transformed material of at least one layer in thematerial bed differs in the FLS of its particles (e.g., powderparticles) from the FLS of the pre-transformed material within at leastone other layer in the material bed. A layer may comprise two or morematerial types at any combination. For example, two or more elementalmetals, at least one elemental metal and at least one alloy; two or moremetal alloys. All the layers of pre-transformed material depositedduring the 3D printing process may be of the same (e.g., substantiallythe same) material composition. In some instances, a metal alloy isformed in situ during the process of transforming at least a portion ofthe material bed. In some instances, a metal alloy is not formed in situduring the process of transforming at least a portion of the materialbed. In some instances, a metal alloy is formed prior to the process oftransforming at least a portion of the material bed. In some instances,a first metal alloy is formed prior to the process of transforming atleast a portion of the material bed and a second (e.g., requested) metalalloy is formed during the transforming of at least a portion of thematerial bed. In the case of a multiplicity (e.g., mixture) ofpre-transformed materials, one pre-transformed material may be used assupport (i.e., supportive powder), as an insulator, as a cooling member(e.g., heat sink), as a precursor in the requested alloy formation, oras any combination thereof.

In some instances, adjacent components in the material bed are separatedfrom one another by one or more intervening layers. In an example, afirst layer is adjacent to a second layer when the first layer is indirect contact with the second layer. In another example, a first layeris adjacent to a second layer when the first layer is separated from thesecond layer by at least one layer (e.g., a third layer). Theintervening layer may be of any layer size.

At times, the pre-transformed material is requested and/orpre-determined for the 3D object. The pre-transformed material can bechosen such that the material is the requested and/or otherwisepredetermined material for the 3D object. A layer of the 3D object maycomprise a single type of material. For example, a layer of the 3Dobject may comprise a single metal alloy type. In some examples, a layerwithin the 3D object may comprise several types of material (e.g., anelemental metal and an alloy, several ally types, several alloy phases,or any combination thereof). In certain embodiments, each type ofmaterial comprises only a single member of that type. For example: asingle member of metal alloy (e.g., Aluminum Copper alloy). In somecases, a layer of the 3D object comprises more than one type ofmaterial. In some cases, a layer of the 3D object comprises more thanone member of a material type.

In some instances, the elemental metal comprises an alkali metal, analkaline earth metal, a transition metal, a rare-earth element metal, oranother metal. The alkali metal can be Lithium, Sodium, Potassium,Rubidium, Cesium, or Francium. The alkali earth metal can be Beryllium,Magnesium, Calcium, Strontium, Barium, or Radium. The transition metalcan be Scandium. Titanium, Vanadium, Chromium, Manganese, Iron, Cobalt,Nickel, Copper, Zinc, Yttrium, Zirconium, Platinum, Gold, Rutherfordium,Dubnium, Seaborgium, Bohrium, Hassium, Meitnerium, Ununbium, Niobium,Iridium, Molybdenum, Technetium, Ruthenium, Rhodium, Palladium, Silver,Cadmium, Hafnium, Tantalum, Tungsten, Rhenium, or Osmium. The transitionmetal can be mercury. The rare-earth metal can be a lanthanide, or anactinide. The lanthanide metal can he Lanthanum, Cerium, Praseodymium,Neodymium, Promethium, Samarium, Europium, Gadolinium, Terbium,Dysprosium, Holmium, Erbium, Thulium, Ytterbium, or Lutetium. Theactinide metal can be Actinium, Thorium, Protactinium, Uranium,Neptunium, Plutonium, Americium, Curium, Berkelium, Californium,Einsteinium, Fermium, Mendelevium, Nobelium, or Lawrencium. The othermetal can he Aluminum, Gallium, Indium, Tin, Thallium, Lead, or Bismuth.

In some instances, the metal alloy comprises an iron based alloy, nickelbased alloy, cobalt based allow, chrome based alloy, cobalt chrome basedalloy, titanium based alloy, magnesium based alloy, copper based alloy,or any combination thereof. The alloy may comprise an oxidation orcorrosion resistant alloy. The alloy may comprise a super alloy (e.g.,Inconel). The super alloy may comprise Inconel 600, 617, 625, 690, 718,or X-750. The metal (e.g., alloy or elemental) may comprise an alloyused for applications in industries comprising aerospace (e.g.,aerospace super alloys), jet engine, missile, automotive, marine,locomotive, satellite, defense, oil & gas, energy generation,semiconductor, fashion, construction, agriculture, printing, or medical.The metal (e.g., alloy or elemental) may comprise an alloy used forproducts comprising a device, medical device (human & veterinary),machinery, cell phone, semiconductor equipment, generators, turbine,stator, motor, rotor, impeller, engine, piston, electronics (e.g.,circuits), electronic equipment, agriculture equipment, gear,transmission, communication equipment, computing equipment (e.g.,laptop, cell phone, i-pad), air conditioning, generators, furniture,musical equipment, art, jewelry, cooking equipment, or sport gear. Theimpeller may be a shrouded (e.g., covered) impeller that is produced asone piece (e.g., comprising blades and cover) during one 3D printingprocess. The 3D object may comprise a blade. The impeller may be usedfor pumps (e.g., turbo pumps). The impeller and/or blade may be any ofthe ones described in U.S. patent application Ser. No. 15/435,128, filedon Feb. 16, 2017; PCT patent application number PCT/US17/18191, filed onFeb. 16, 2017; or European patent application number. EP17156707.6,filed on Feb. 17, 2017, all titled “ACCURATE THREE-DIMENSIONALPRINTING,” each of which is incorporated herein by reference in itsentirety where non-contradictory. The metal (e.g., alloy or elemental)may comprise an alloy used for products for human and/or veterinaryapplications comprising implants, or prosthetics. The metal alloy maycomprise an alloy used for applications in the fields comprising humanand/or veterinary surgery, implants (e.g., dental), or prosthetics.

In some instances, the alloy includes a superalloy. The alloy mayinclude a high-performance alloy. The alloy may include an alloyexhibiting at least one of excellent mechanical strength, resistance tothermal creep deformation, good surface stability, resistance tocorrosion, and resistance to oxidation. The alloy may include aface-centered cubic authentic crystal structure. The alloy may compriseHastelloy. Inconel, Waspaloy, Rene alloy (e.g., Rene-80, Rene-77,Rene-220, or Rene-41). Haynes alloy, Incoloy, MP98T, TMS alloy. MTEK(e.g., MTEK grade MAR-M-247, MAR-M-509, MAR-M-R41, or MAR-M-X-45), orCMSX (e.g., CMSX-3, or CMSX-4). The alloy can be a single crystal alloy.

In some instances, the iron alloy comprises Elinvar, Fernico,Ferroalloys, Invar, Iron hydride, Kovar, Spiegeleisen, Staballoy(stainless steel), or Steel. In some instances, the metal alloy issteel. The Ferroalloy may comprise Ferroboron, Ferrocerium, Ferrochrome,Ferromagnesium, Ferromanganese, Ferromolybdenum, Ferronickel,Ferrophosphorus, Ferrosilicon, Ferrotitanium, Ferrouranimn, orFerrovanadimn. The iron alloy may comprise cast iron, or pig iron. Thesteel may comprise Bulat steel, Chromoly. Crucible steel, Damascussteel, Hadfield steel. High speed steel, HSLA steel, Maraging steel,Maraging steel (M300). Reynolds 531, Silicon steel, Spring steel,Stainless steel, Tool steel, Weathering steel, or Wootz steel. Thehigh-speed steel may comprise Mushet steel. The stainless steel maycomprise AL-6XN, Alloy 20, celestrium, marine grade stainless,Martensitic stainless steel, surgical stainless steel, or Zeron 100. Thetool steel may comprise Silver steel. The steel may comprise stainlesssteel. Nickel steel, Nickel-chromium steel, Molybdenum steel. Chromiumsteel. Chromium-vanadium steel, Tungsten steel,Nickel-chromium-molybdenum steel, or Silicon-manganese steel. The steelmay be comprised of any Society of Automotive Engineers (SAE) gradesteel such as 440F, 410, 312, 430, 440A, 440B, 440C, 304, 305, 304L,304L, 301, 304LN, 301LN, 2304, 316, 316L, 316LN, 316, 316LN, 316L, 316L,316, 317L, 2205, 409, 904L, 321, 254SMO, 316Ti, 321H, or 304H. The steelmay comprise stainless steel of at least one crystalline structureselected from the group consisting of authentic, superaustenitic,ferritic, martensitic, duplex, and precipitation-hardening martensitic.Duplex stainless steel may be lean duplex, standard duplex, superduplex, or hyper duplex. The stainless steel may comprise surgical gradestainless steel (e.g., authentic 316, martensitic 420, or martensitic440). The authentic 316 stainless steel may comprise 316L, or 316LVM.The steel may comprise 17-4 Precipitation Hardening steel (e.g., type630, a chromium-copper precipitation hardening stainless steel, 17-4PHsteel).

In some instances, the titanium-based alloy comprises alpha alloy, nearalpha alloy, alpha and beta alloy, or beta alloy. The titanium alloy maycomprise grade 1, 2, 2H, 3, 4, 5, 6, 7.7H, 8, 9, 10, 11, 12, 13, 14, 15,16, 16H, 17, 18, 19, 20, 21.2, 23, 24, 25, 26, 26H, 27, 28, 29, 30, 31,32, 33, 34, 35, 36, 37, 38, or higher. In some instances, the titaniumbase alloy comprises Ti-6Al-4V or Ti-6Al-7Nb.

In some instances, the Nickel alloy comprises Alnico, Alumel, Chromel,Cuprordckel, Ferronickel, German silver, Hastelloy, Inconel, Monelmetal, Nichrome, Nickel-carbon, Nicrosil, Nisil, Nitinol, orMagnetically “soft” alloys. The magnetically “soft” alloys may compriseMu-metal, Pumalloy, Supemralloy, or Brass. The brass may comprise Nickelhydride, Stainless or Coin silver. The cobalt alloy may compriseMegallium, Stellite (e.g., Talonite), Ultima, or Vitallium. The chromiumalloy may comprise chromium hydroxide, or Nichrome.

In some instances, the aluminum alloy comprises AA-8000, Al—Li(aluminum-lithium), Alnico, Duralumin, Hidumiuium, Kryron Magnalium,Nantbe, Scandium--aluminum, or Y alloy. The magnesium alloy may compriseElektron, Magnox, or T—Mg—Al—Zn (Bergman phase) alloy.

In some instances, the copper alloy comprises Arsenical copper,Beryllium copper, Billon, Brass, Bronze, Constantin, Copper hydride,Copper-tungsten, Corinthian bronze, Cunife, Cupronickel, Cymbal alloys,Devarda's alloy, Electrum, Hepatizon, Heusler alloy, Manganin,Molybdochalkos, Nickel silver, Nordic gold, Shakudo, or Tumbaga. TheBrass may comprise Calamine brass, Chinese silver, Dutch metal, Gildingmetal, Muntz metal, Pinchbeck, Prince's metal, or Tombac. The Bronze maycomprise Aluminum bronze, Arsenical bronze, Bell metal, Florentinebronze, Guanin, Gunmetal, Glucydur, Phosphor bronze, Ormolu, or Speculummetal. The copper alloy may be a high-temperature copper alloy (e.g.,GRCop-84).

In some instances, the metal alloys are Refractory Alloys. Therefractory metals and alloys may be used for heat coils, heatexchangers, furnace components, or welding electrodes. The RefractoryAlloys may comprise a high melting points, low coefficient of expansion,mechanically strong, low vapor pressure at elevated temperatures, highthermal conductivity, or high electrical conductivity.

In some examples, the material (e.g., pre-transformed material)comprises a material wherein its constituents (e.g., atoms or molecules)readily lose their outer shell electrons, resulting in a free-flowingcloud of electrons within their otherwise solid arrangement. In someexamples the material is characterized in having high electricalconductivity, low electrical resistivity, high thermal conductivity, orhigh density (e.g., as measured at ambient temperature (e.g., R.T., or20° C.)). The high electrical conductivity can be at least about 1*10⁵Siemens per meter (S/m), 5*10⁵ S/m, 1*10⁶ S/m, 5*10⁶ S/m, 1*10⁷ S/m,5*10⁷ S/m, or 1*10⁸ S/m. The symbol “*” designates the mathematicaloperation “times,” or “multiplied by.” The high electrical conductivitycan be any value between the afore-mentioned electrical conductivityvalues e.g., from about 1*10⁵ S/m to about 1*10⁸ S/m). The lowelectrical resistivity may be at most about 1*10⁻⁵ ohm times meter(Ω*m), 5*10⁻⁶ Ω*m, 1*10⁻⁶ Ω*m, 5*10⁻⁷ Ω*m, 1*10⁻⁷ Ω*m, 5*10⁻⁸, or 1*10⁻⁸Ω*m. The low electrical resistivity can be any value between theafore-mentioned electrical resistivity values (e.g., from about 1×10⁻⁵Ω*m to about 1×10⁻⁸ Ω*m). The high thermal conductivity may be at leastabout 20 Watts per meters times Kelvin (W/mK), 50 W/mK, 100 W/mK, 150W/mK, 200 W/mK, 205 W/mK, 300 W/mK, 350 W/mK, 400 W/mK, 450 W/mK, 500W/mK, 550 W/mK, 600 W/mK, 700 W/mK, 800 W/mK, 900 W/mK, or 1000 W/mK.The high thermal conductivity can be any value between theafore-mentioned thermal conductivity values (e.g., from about 20 W/mK toabout 1000 W/mK). The high density may be at least about 1.5 grams percubic centimeter (g/cm³), 2 g/cm³, 3 g/cm³, 4 g/cm³, 5 g/cm³, 6 g/cm³, 7g/cm³, 8 g/cm³, 9 g/cm³, 10 g/cm³, 11 g/cm³, 12 g/cm³, 13 g/cm³, 14g/cm³, 15 g/cm³, 16 g/cm³, 17 g/cm³, 18 g/cm³, 19 g/cm³, 20 g/cm³, or 25g/cm³. The high density can be any value between the afore-mentioneddensity values (e.g., from about 1 g/cm³ to about 25 g/cm³).

At times, a metallic material (e.g., elemental metal or metal alloy)comprises small amounts of non-metallic materials, such as, for example,oxygen, sulfur, or nitrogen. In some cases, the metallic material cancomprise the non-metallic material in a trace amount. A trace amount canbe at most about 100000 parts per million (ppm), 10000 ppm, 1000 ppm,500 ppm, 400 ppm, 200 ppm, 100 ppm, 50 ppm, 10 ppm, 5 ppm, or 1 ppm(based on weight, w/w) of non-metallic material. A trace amount cancomprise at least about 10 ppt, 100 ppt, 1 ppb, 5 ppb, 10 ppb, 50 ppb,100 ppb, 200 ppb, 400 ppb, 500 ppb, 1000 ppb, 1 ppm, 10 ppm, 100 ppm,500 ppm. 1000 ppm, or 10000 ppm (based on weight, (w/w) of non-metallicmaterial. A trace amount can be any value between the afore-mentionedtrace amounts (e.g., from about 10 parts per trillion (ppt) to about100000 ppm, from about 1 ppb to about 100000 ppm, from about 1 ppm toabout 10000 ppm, or from about 1 ppb to about 1000 ppm).

In some embodiments, 3D printing methodologies are employed for printingan object that is substantially two-dimensional, such as a wire or aplanar object. The 3D object may comprise a plane like structure(referred to herein as “planar object,” “three-dimensional plane,” or“3D plane”). The 3D plane may have a relatively small width as opposedto a relatively large surface area. The 3D plane may have a relativelysmall height relative to its width and length. For example, the 3D planemay have a small height relative to a large horizontal plane. FIG. 4shows an example of a 3D plane that is substantially planar (e.g.,flat). The 3D plane may be planar, curved, or assume an amorphous 3Dshape. The 3D plane may be a strip, a blade, or a ledge. The 3D planemay comprise a curvature. The 3D plane may be curved. The 3D plane maybe planar (e.g., flat). The 3D plane may have a shape of a curvingscarf. The term “3D plane” is understood herein to be a generic (e.g.,curved) 3D surface. For example, the 3D plane may be a curved 3Dsurface. The one or more layers within the 3D object may besubstantially planar (e.g., flat). The planarity of a surface or aboundary the layer may be (e.g., substantially) uniform Substantiallyuniform may be relative to the intended purpose of the 3D object Theheight of the layer at a particular position may be compared to anaverage layering plane. The layering plane can refer to a plane that alayer of the 3D object is (e.g., substantially) oriented duringprinting. A boundary between two adjacent (printed) layers of hardenedmaterial of the 3D object may define a layering plane. The boundary maybe apparent by, for example, one or more melt pool terminuses (e.g.,bottom or top). A 3D object may include multiple layering planes (e.g.,corresponding to each layer). In some embodiments, the layering planesare (e.g., substantially) parallel to one another. An average layeringplane may be defined by a linear regression analysis (e.g., leastsquares planar fit of the top-most part of the surface of the layer ofhardened material). An average layering plane may be a plane calculatedby averaging the material height at each selected point on the topsurface of the layer of hardened material. The selected points may bewithin a specified region of the 3D object. The deviation from any pointat the surface of the planar layer of hardened material may be at most20% 15%, 10%, 5%, 3%, 1%, or 0.5% of the height (e.g., thickness) of thelayer of hardened material. FIG. 48 shows a schematic example of avertical cross section of a portion of a 3D object having layers 4800,4802 4804 and 4816 of hardened material, with each layer sequentiallyformed during the 3D printing process. Boundaries (e.g., 4806, 4808,4810 and 4812) between the layers may be (e.g., substantially) planar,The boundaries between the layers may have; some irregularity (e.g.,roughness) due to the transformation (e.g., melting) process. An averagelayering plane (e.g., 4814) may correspond to a (e.g., imaginary) planethat is calculated or estimated as an average layering plane thereof.

The substantially planar one or more layers may have a large radius ofcurvature. FIG. 7 shows an example of a vertical cross section of a 3Dobject (e.g., 712, 713, 714) comprising (e.g., substantially) planarlayers (e.g., 712, layers numbers 1-4) and non-planar layers (e.g., 712layers number 5-6; 713 layers number 1-6; or 714 layers number 5-6) thathave a radius of curvature. An average layering plane of layers that arenon-planar (e.g., 712, layers number 5-6; 713, layers number 1-6; or714, layers number 5-6) may correspond to a plane that is calculated(e.g., by linear regression analysis) from the non-planar layer. FIG. 7,716 and 717 are super-positions of curved layer on a circle 715 having aradius of curvature “r.” The one or more layers may have a radius ofcurvature equal to the radius of curvature of the layer surface. Theradius of curvature may equal infinity (e.g., when the layer is (e.g.,substantially) planar). The radius of curvature of at least one thelayer of the 3D object (e.g., all the layers of the 3D object, thebottom skin layer, and/or the overhang) may have a value of at leastabout 0.1 centimeter (cm), 0.2 cm, 0.3 cm, 0.4 cm, 0.5 cm, 0.6 cm, 0.7cm, 0.8 cm, 0.9 cm, 1 cm, 3 cm, 5 cm, 10 cm, 20 cm, 30 cm, 40 cm, 50 cm,60 cm, 70 cm, 80 cm, 90 cm, 1 meter (m), 1.5 m, 2 m, 2.5 m, 3 m, 3.5 m,4 m, 4.5 m, 5 m, 10 m, 15 m, 20 m, 25 m, 30 m, 50 m, or 100 m. Theradius of curvature of at least one layer of the 3D object (e.g., allthe layers of the 3D object) may have any value between any of theafore-mentioned values of the radius of curvature (e.g., from about 10cm to about 90 m, from about 50 cm to about 10 m, from about 5 cm toabout 1 m, from about 50 cm to about 5 m, from about 5 cm to infinity,or from about 40 cm to about 50 m). In some embodiments, a layer with aninfinite radius of curvature is a layer that is planar. In someexamples, the one or more layers may be included in a planar section ofthe 3D object, or may be a planar 3D object (e.g., a flat plane, or 3Dplane). In some instances, part of at least one layer within the 3Dobject may have any of the radii of curvature mentioned herein, whichwill designate the radius of curvature of that layer portion. The 3Dobject may comprise a hanging structure. The hanging structure may be aplane like structure (e.g., a 3D plane).

The radius of curvature, “r,” of a curve at a point can be a measure ofthe radius of the circular arc (e.g., FIG. 7, 716) which bestapproximates the curve at that position. The radius of curvature can bethe inverse of the curvature. In the case of a 3D curve (also herein a“space curve”), the radius of curvature may be the length of thecurvature vector. The curvature vector can comprise of a curvature(e.g., the inverse of the radius of curvature) having a particulardirection. For example, the particular direction can be the directiontowards the platform (e.g., designated herein as negative curvature), oraway from the platform (e.g., designated herein as positive curvature).For example, the particular direction can be the direction towards thedirection of the gravitational field (e.g., designated herein asnegative curvature), or opposite to the direction of the gravitationalfield (e.g., designated herein as positive curvature). A curve (alsoherein a “curved line”) can be an object similar to a line that is notrequired to be straight. A straight line can be a special case of curvedline wherein the curvature is (e.g., substantially) zero. A line of(e.g., substantially) zero curvature has an (e.g., substantially)infinite radius of curvature. A curve can be in two-dimensions (e.g.,vertical cross section of a plane), or in three-dimension (e.g.,curvature of a plane). The curve may represent a cross section of acurved plane. A straight line may represent a cross section of a flat(e.g., planar) plane. The platform may be a building platform. Theplatform may comprise the substrate, base, or bottom of the enclosure.The material bed may be operatively coupled and/or disposed adjacent to(e.g., on) the platform

In some embodiments, the 3D object comprises one or more layering planesN of the layered structure. A layering plane can be used to refer to anorientation of a layer of the 3D object during its printing. In someembodiments, a layering plane is (e.g., substantially) parallel to thesupport surface of the platform, (e.g., substantially) parallel to theexposed surface of the material bed, and/or (e.g., substantially)orthogonal (e.g., perpendicular) to the gravitational field vector. Thelayering plane may be the average or mean plane of a layer of hardenedmaterial (as part of the 3D object). The 3D object may comprise points Xand Y, which reside on the surface of the 3D object. FIG. 10 shows anexample of points X and Y on the surface of a 3D object. In someembodiments, X is spaced apart from Y by the auxiliary feature spacingdistance. A sphere of radius XY that is centered at X lacks one or moreauxiliary supports or one or more auxiliary support marks that areindicative of a presence or removal of the one or more auxiliary supportfeatures. An acute angle between the straight line XY and the directionnormal to N may be from about 45 degrees to about 90 degrees. The acuteangle between the straight line XY and the direction normal to thelayering plane may be of the value of the acute angle alpha. When theangle between the straight line XY and the direction of normal to N isgreater than 90 degrees, one can consider the complementary acute angle.The layer structure may comprise any material(s) used for 3D printing.Each layer of the 3D structure (e.g., 3D object) can he made of a singlematerial or of multiple materials. Sometimes one part of the 3D object(e.g., one layer of the 3D object) may comprise one material, andanother part may comprise a second material different than the firstmaterial. A layer of the 3D object may be composed of a compositematerial. The 3D object may be composed of a composite material. The 3Dobject may comprise a functionally graded material. In some cases, theorientation of the layering plane can be identified in a 3D object byinspection (e.g., using X-ray, optical microscopy, scanning electronmicroscopy and/or tunneling electron microscopy). For example, a surfaceof the object may include ridges (also referred to as steps) (e.g., FIG.58A, 5801), with each ridge corresponding to a layer of hardenedmaterial. In some cases, successively deposited melt pools may form thelayer of hardened material. In some cases, a series of melt pools (e.g.,successively deposited melt pools) within a layer of the 3D object maybe oriented in accordance (e,g., (e.g., substantially) parallel) withrespect to a layering plane. FIG. 25A shows an example of melt pools2507, 2508 and 2509 as part of a layer 2525 formed in accordance with(e.g., (e.g., substantially) parallel to) a layering plane (e,g,parallel to trajectory 2530). The layering plane may be (e.g.,substantially) perpendicular to the build direction of the object duringits printing.

A layering plane of a 3D object may be at any angle with respect to asurface of the build platform surface and/or a surface of the 3D object.The angle may reveal the angle at which the object (or a portion of theobject) was oriented with respect to the surface of the build platform.FIG. 47A shows an example 3D object 4720 that is formed (e.g.,substantially) horizontally on a platform 4722 and/or (e.g.,substantially) vertically with respect to the gravity vector 4723. Theresulting layers (e.g., 4721) of hardened material can be (e.g.,substantially) parallel with respect to each other (e.g., in accordancewith an average layering plane). Adjacent layers may be integrallycoupled with (e.g., chemically (e.g., metallically) bonded) with eachother during the transformation (e.g., melting) process. The layers mayhe oriented (e.g., substantially) horizontally with respect to a bottomsurface (e.g., 4726) and/or a top surface (e.g., 4728) of the 3D object.The layers may be oriented (e.g., substantially) vertically with respectto a side surface (e.g., 4724 or 4725) of the 3D object. FIG. 47B showsan example of a 3D object 4740 that is formed at an angle alpha (α)relative to the surface of a platform 4742 and/or an angle of 90 degreesplus alpha (α) with respect to the gravity vector 4743. The resultinglayers (e.g., 4741) of hardened material may be at the angle alpha (α)with respect to a bottom surface (e.g., 4746) and/or top surface (e.g.,4748) of the 3D object. The layers may be oriented an angle of 90degrees plus alpha (α) with respect to a side surface (e.g., 4744 or4745) of the 3D object.

In some embodiments, the 3D object is generated with respect to a (e.g.,virtual) model of a requested 3D object. The 3D object model maycomprise a simulated model. The model may be a computer-generated model.In some embodiments, the generated 3D object may be generated with theaccuracy of at least about 5 μm, 10 μm, 15 μm, 20 μm, 25 μm, 30 μm, 35μm, 40 μm, 45 μm, 50 μm, 55 μm, 60 μm, 65 μm, 70 μm, 75 μm, 80 μm, 85μm, 90 μm, 95 μm, 100 μm, 150 μm, 200 μm, 250 μm, 300 μm, 400 μm, 500μm, 600 μm, 700 μm, 800 μm, 900 μm, 1000 μm, 1100 μm, or 1500 μm withrespect to a model of the requested 3D object. With respect to a modelof the requested 3D object, the generated 3D object may be generatedwith the accuracy of any accuracy value between the afore-mentionedvalues (e.g., from about 5 μm to about 100 μm, from about 15 μm to about35 μm, from about 100 μm to about 1500 μm, from about 5 μm to about 1500μm, or from about 400 μm to about 600 μm).

In some embodiments, the hardened layer of transformed material deformsthe 3D printing and/or upon hardening). The deformation may cause ahorizontal (e.g., height) and/or vertical g, width and/or length)deviation from a requested uniformly planar layer of hardened material.The horizontal and/or lateral deviation of the planar surface of thelayer of hardened material may be of at most about 100 μm, 90 μm, 80, 70μm, 60 μm, 50 μm, 40 μm, 30 μm, 20 μm, 10 μm, or 5 μm. The horizontaland/or vertical deviation of the planar surface of the layer of hardenedmaterial may be any value between the afore-mentioned height deviationvalues (e.g., from about 100 μm to about 5 μm, from about 50 μm to about5 μm, from about 30 μm to about 5 μm, or from about 20 μm to about 5μm). The height uniformity (e.g., of the uniformly planar layer) maycomprise high precision uniformity. The resolution of the 3D object maybe at least about 100 dots per inch (dpi), 300 dpi, 600 dpi, 1200 dpi,2400 dpi, 3600 dpi, or 4800 dpi. The resolution of the 3D object may beat most about 100 dpi, 300 dpi, 600 dpi, 1200 dpi, 2400 dpi, 3600 dpi,or 4800 dpi. The resolution of the 3D object may be any value betweenthe afore-mentioned values (e.g., from 100 dpi, to 4800 dpi, from 300dpi to 2400 dpi, or from 600 dpi, to 4800 dpi). A dot may be a meltpool. A dot may be a (e.g., vertical) step. A dot may be a height of thelayer of hardened material. A step may have a value of at most theheight of the layer of hardened material. The vertical (e.g., height)uniformity of a layer of hardened material may persist across a portionof the layer surface that has a FLS (e.g., a width and/or a length) ofat least about 1 mm, 2 mm, 3 rum, 4 mm, 5 mm, or 10 mm, have a heightdeviation of at least about 10 mm, 9 mm, 8 mm, 7 mm, 6 mm, 5 mm, 4 mm, 3mm, 2 mm, 1 mm, 500 μm, 400 μm, 300 μm, 200 μm, 100 μm, 90 μm, 80 μm, 70μm, 60 μm, 50 μm, 40 μm, 30 μm, 20 μm, or 10 μm. The height uniformityof a layer of hardened material may persist across a portion of thetarget surface that has a FLS (e.g., a width and/or a length) of mostabout 10 mm, 9 mm, 8 mm, 7 mm, 6 mm, 5 mm, 4 mm, 3 mm, 2 mm, 1 mm, 500μm, 400 μm, 300 μm, 200 μm, 100 μm, 90 μm, 80, 70 μm, 60 μm, 50 μm, 40μm, 30 μm, 20 μm, or 10 μm. The height uniformity of a layer of hardenedmaterial may persist across a portion of the target surface that has aFLS (e.g., a width and/or a length) of any value between theafore-mentioned width or length values (e.g., from about 10 mm to about10 μm, from about 10 mm to about 100 μm, or from about 5 mm to about 500μm). A target surface may be a layer of hardened material (e.g., as partof the 3D object).

In an aspect, a 3D object (e.g., FIG. 1, 106) is generated from apre-transformed material by irradiating a portion of a material bed(e.g., 104) comprising the pre-transformed material (e.g., by using anenergy beam, e.g., 101 or 108). The irradiation may transform a portionof the irradiated material bed into a transformed material. The energybeam may be directed at a target surface, such as an exposed surface(e.g., FIG. 1, 131) of the material bed. The transformed material mayform at least a portion of the 3D object. In some examples, thetransformed material may harden to form a hardened material that is atleast a portion of the 3D object. In some examples, the transformedmaterial forms the hardened material that is at least a portion of the3D object. The target surface may include a surface of thepre-transformed material (e.g., a layer of powder) and/or a surface ofan already transformed material (e.g., a hardened portion of the 3Dobject (e.g., FIG. 1. 106)). The area of the target surface that theenergy beam impinges on can be referred to as the spot size or footprintof the energy beam at the target surface.

In some embodiments, at least a portion of the 3D object is dense (e.g.,substantially fully dense, e.g., FIG. 15D, 1535). Substantially isrelative to the intended purpose of the 3D object. In embodiments, the3D object comprises pores (e.g., FIG. 15B, 1515). In some embodiments, aportion of the 3D object may be dense and another portion may be porous.The pores may be random or systematic. The porous portion of the 3Dobject (e.g., PMX) may be permeable. One or more porous portions of the3D object may have a different amount of porosity (e.g., at least about30%, 40% porosity v/v, or area/area porosity, e.g., of a cross-sectionalplane of maximum porosity). One or more porous portions may have (e.g.,substantially) the same amount of porosity. Dense portion of the 3Dobject may comprise a greater amount of transformed material than aporous portion of the 3D object. Dense may comprise heavily packedtransformed material than a porous portion of the 3D object. Dense maycomprise less permeable transformed matter than a porous portion of the3D object. In some examples, the at least a portion of the 3D object mayform a porous matrix (e.g., 1515). The porous matrix may be formed by atleast one 3D printing process e.g., additive manufacturing, or directmaterial deposition). For example, the porous matrix layer may be formedby sintering and/or melting a pre-transformed material to form atransformed material. The porous matrix may be formed by heating,pressurizing a pre-transformed material to form a transformed material.A transforming energy beam (e.g., type-1 energy beam or type-2 energybeam), e.g., FIG. 15B, 1510) may be used to form the porous matrix(e.g., 1515). The pre-transformed material (e.g., FIG. 15A, 1505) may beflowable during the formation of the 3D object (e.g., during thetransformation and/or hardening operations). The 3D object (e.g., porous3D object) may be comprise a rigid structure that is not flowable. Forexample, the porous 3D object portion may be a porous matrix. In someexamples, formation of the porous matrix portion may be a stage in theformation of a dense 3D object portion. For example, the porous matrixmay comprise a hardened material. The porous matrix may further comprisepre-transformed material. In some examples, pre-transformed material isadded to the formed porous matrix (e.g., using a material dispensingmechanism), for example, prior to its transformation and/ordensification. The hardened and/or pre-transformed material of theporous matrix may be transformed (e.g., using an energy beam. E.g., FIG.15C, 1521) to form a denser 3D object (e.g., a 3D object that has agreater density than the porous matrix. E.g., FIG. 15D, 15:35). Thetransformation of the PMX (e.g., FIG. 15C, 1520) may comprise forming amelt pool (e.g., FIG. 15C, 1523) by irradiating a portion of thematerial bed (e.g., 1522) with a transforming energy beam (e.g., 1521).The PMX (e.g., 1515) and/or dense portion (e.g., 1535) may be suspendedanchorlessly in the material bed during the 3D printing.

In an aspect, a 3D object is generated by disposing a (e.g.,substantially) planar layer of pre-transformed material above (e.g., on)a platform (e.g., build platform) to form a material bed (e.g., FIG. 1,104). At times, the 3D object may be generated by disposing a planarlayer of pre-transformed matter on the base (e.g., FIG. 1, 102) on whichthe substrate (e.g., FIG. 1, 109) or the material bed may be disposed.At least a portion of the particulate material in the material bed maybe irradiated by an energy beam (e.g., 101, 108) to form a transformedmaterial as part of the 3D object. The transformed material maysubsequently harden to form at least a portion of the 3D object. Thetransformed material may form the harden material as part of the 3Dobject. Optionally, a process of disposing a planar layer ofpre-transformed material (e.g., by lowering the platform, dispensing aparticulate material, and planarizing the dispensed particulatematerial), irradiating a portion of the material bed to (e.g.,subsequently or directly) form the hardened material my repeat until arequested 3D object is printed layer by layer (e.g., additively,layerwise). A printed 3D object may include a plurality of layers thatare indicative of a layerwise forming (e.g., printing) of the 3D object.

In some examples, the 3D object is a large 3D object. In someembodiments, the 3D object comprises a large hanging structure (e.g.,wire, ledge, or shell). Large may be a 3D object having a FLS of atleast about 1 centimeter (cm), 1.5 cm, 2 cm, 10 cm, 20 cm, 30 cm, 40 cm,50 cm, 60 cm, 70 cm, 80 cm, 90 cm, 1 m, 2 m, 3 m, 4 m, 5 m, 10 m, 50 m,80 m, or 100 m. The hanging structure may be a (e.g., vertically) thinstructure. The hanging structure may be a plane like structure (referredto herein as “three-dimensional plane,” or “3D plane”). The 3D plane mayhave a relatively small width as opposed to a relatively large surfacearea. For example, the 3D plane may have a small height relative to alarge horizontal plane. FIG. 4 shows an example of a 3D plane that isplanar. The 3D plane may be planar, curved, or assume an amorphous 3Dshape. The 3D plane may be a strip, a blade, or a ledge. The 3D planemay comprise a curvature. The 3D plane may be curved. The 3D plane maybe planar (e.g., flat). The 3D plane may have a shape of a curvingscarf.

In some embodiments, the 3D object comprises a first portion and asecond portion. The first portion may be connected to a rigid-portion(e.g., core) at one, two, or three sides (e.g., as viewed from the top).The rigid-portion may be the rest of the 3D object. The second portionmay be connected to the rigid-portion at one, two, or three sides (e.g.,as viewed from the top). For example, the first and second portion maybe connected to a rigid-portion (e.g., column, post, or wall) of the 3Dobject. For example, the first and second portion may be connected to anexternal cover that is a part of the 3D object. The first and/or secondportion may be a wire or a 3D plane. The first and/or second portion maybe different from a wire or 3D plane. The first and/or second portionmay be a blade (e.g., turbine or impeller blade). The first and secondportions may be (e.g., substantially) identical in terms of structure,geometry, volume, and/or material composition. The first and secondportions may be (e.g., substantially) identical in terms of structure,geometry, volume, material composition, or any combination thereof. Thefirst portion may comprise a top surface. Top may be in the directionaway from the platform and/or opposite to the gravitational field. Thesecond portion may comprise a bottom surface (e.g., bottom skinsurface). Bottom may be in the direction towards the platform and/or inthe direction of the gravitational field.

FIG. 5 shows an example of a first (e.g., top) surface 510 and a second(e.g., bottom) surface 520. At least a portion of the first and secondsurface are separated by a gap. At least a portion of the first surfaceis separated by at least a portion of the second surface (e.g., toconstitute a gap). The gap may be filled with pre-transformed ortransformed (e.g., and subsequently hardened) material, e.g., during theformation of the 3D object. The second surface may be a bottom skinlayer. FIG. 5 shows an example of a vertical gap distance 540 thatseparates the first surface 510 from the second surface 520. Thevertical gap distance may be equal to the vertical distance of the gapas disclosed herein. Point. A (e.g., in FIG. 5) inlay reside on the topsurface of the first portion. Point B may reside on the bottom surfaceof the second portion. The second portion may be a cavity ceiling orhanging structure as part of the 3D object. Point B (e.g., in FIG. 5)may reside above point A. The gap may be the (e.g., shortest) distance(e.g., vertical distance) between points A and B. FIG. 5 shows anexample of the gap 540 that constitutes the shortest distance d_(AR)between points A and B. There may be a first normal to the bottomsurface of the second portion at point B. FIG. 5 shows an example of afirst normal 512 to the surface 520 at point B. The angle between thefirst normal 512 and a direction of the gravitational accelerationvector 500 (e.g., direction of the gravitational field) may be any angleγ. Point C may reside on the bottom surface of the second portion. Theremay be a second normal to the bottom surface of the second portion atpoint C. FIG. 5 shows an example of the second normal 522 to the surface520 at point C. The angle between the second normal 522 and thedirection of the gravitational acceleration vector 500 may be any angleδ. Vectors 511, and 521 are parallel to the gravitational accelerationvector 500. The angles γ and δ may be the same or different. The anglebetween the first normal 512 and/or the second normal 522 to thedirection of the gravitational acceleration vector 500 may be any anglealpha. The angle between the first normal 512 and/or the second normal522 with respect to the normal to the substrate (e.g., platform) may beany angle alpha disclosed herein. The angle between the first normal 512and/or the second normal 522 with respect to the normal to the substrate(e.g., platform) may be any angle disclosed herein for the angledstructure. The angles γ and δ may be any angle alpha. The angles γ and δmay be any of any angled structure (e.g., acute, or obtuse). Forexample, alpha may be at most about 45°, 40°, 30°, 20°, 10°, 5°, 3°, 2°,1°, or 0.5°. The shortest distance between points B and C may be anyvalue of the auxiliary support feature spacing distance mentionedherein. For example, the shortest distance BC (e.g., d_(BC)) may be atleast about 0.1 millimeters (mm), 0.5 mm, 1 mm, 1.5 mm, 2 mm, 3 mm, 4mm, 5 mm, 10 mm, 15 mm, 20 mm, 25 mm, 30 mm 35 mm, 40 mm, 50 mm, 100 mm.200 mm, 300 mm, 400 mm, or 500 mm. As another example, the shortestdistance BC may be at most about 500 mm, 400 mm, 300 mm, 200 mm, 100 mm,50 mm, 40 mm, 35 mm, 30 mm, 25 mm, 20 mm, 15 mm, 10 mm, 5 mm 4 mm, 3 mm,2 mm, 1.5 mm, 1 mm, 0.5 mm, or 0.1 mm. FIG. 5 shows an example of theshortest distance BC (e.g., 530, d_(BC)). The bottom skin layer may bethe first surface and/or the second surface. The bottom skin layer maybe the first formed layer of the 3D object. The bottom skin layer may bethe first formed hanging layer in the 3D object (e.g., that is separatedby a gap from a previously formed layer of the 3D object). The verticaldistance of the gap may be at least about 30 μm, 35 μm, 40 μm, 50 μm, 60μm, 70 μm, 80 μm, 90 μm, 100 μm, 150 μm, 200 μm, 0.05 mm, 0.1 mm, 0.25mm, 0.5 mm, 1 mm, 2 mm, 3 mm, 4 mm, 5 mm, 6 mm, 7 mm, 8 mm, 9 mm, or 10mm. The vertical distance of the gap may be at most about 0.05 mm, 0.1mm, 0.25 mm, 0.5 mm, 1 mm, 2 mm, 3 mm, 4 mm, 5 mm, 6 mm, 7 mm, 8 mm, 9mm, 10 mm, or 20 mm. The vertical distance of the gap may be any valuebetween the afore-mentioned values (e.g., from about 30 μm to about 200μm, from about 100 μm to about 200 μm, from about 30 μm to about 100 mm,from about 80 mm to about 150 mm, from about 0.05 mm to about 20 mm,from about 0.05 mm to about 0.5 mm, from about 0.2 mm to about 3 mm,from about 0.1 mm to about 10 mm, or from about 3 mm to about 20 mm).

In some cases, a 3D object comprises multiple bottom skin layers (e.g.,bottoms of turbine blades). A 3D object may comprise structures such ascavities, gaps, wires, ledges, or 3D planes. A structure within aforming 3D object may comprise a bottom skin layer (e.g., that is formedabove a pre-transformed material without auxiliary support, or withspaced apart auxiliary supports). At times, at least two of thestructures may have similar geometry. At times, at least two of thestructures may have a different geometry. At times, the one of thestructures may connect portions of the 3D object. At times, thestructures may be separated by a gap. For example, multiple blades of aturbine may be separated by a gap between a first blade portion and asecond blade portion. For example, a first portion (e.g., a bladestructure) of the 3D object (e.g., a turbine) may comprise a firstbottom skin layer followed by one or more layers that form the firstportion, and a second portion (e.g., a second blade structure) of the 3Dobject (e.g., a turbine) may comprise a second bottom skin layerfollowed by one or more layers that form the second portion of the 3Dobject. At times, the first portion and the second portion of the 3Dobject may be connected by a third portion (e.g., a ledge structure) toform the 3D object. FIGS. 6A-6B show examples of a first portion and/ora second portion of a 3D object that ate connected to one or morerigid-portions. FIG. 6C shows an example of a first portion of a 3Dobject, which first portion comprises a bottom skin layer, that is notconnected to a rigid-portion, and that is suspended anchorlessly in thematerial bed. FIG. 6A shows an example of a first portion (e.g., 640)and a second portion (e.g., 645) of a 3D object disposed at an angleperpendicular (e,g, 90 degrees. 642, 644) to at least one rigid-portionof the 3D object (e.g., two rigid portions 618, and 682). FIG. 6B showsan example of a first portion (e.g., 660) and a second portion (e.g.,665) of a 3D object (e.g., two blades of a propeller) forming an angle(e.g., 652, 654) that is not perpendicular to the rigid portion of the3D object (e.g., 620). At times, the first portion and the secondportion may not be connected to a portion of the 3D object (e.g., to arigid-portion. E.g., FIG. 6C). The first portion may comprise one ormore layers (e.g. 610, 612, 614, 628, 630, and 632). The second portionmay comprise one or more layers (e.g., 602, 604, 606, 622, 624, and626). The layer may include pre-transformed material (e.g., particulatematerial). The layer may include a porous matrix. The layer may includetransformed (e.g., hardened) material. The layer may include a PMX thathas been transformed to form a denser layer of transformed material. Thefirst layer for the first and/or second portions of the 3D object may bea bottom skin layer (e.g., 602, 610, 622, and 628). The bottom skinlayer (e.g., 690, 628, 676, 610, and 602) may be a transformed materiallayer. At times, the bottom skin layer may be parallel to the targetsurface. At times, the bottom skin layer may be at an angle (e.g., ashallow angle, steep angle, or an intermediate angle) relative to thetarget surface (e.g., an exposed surface of the material bed and/or thesupport surface of the platform) and/or a (e.g., average) layering planeof the object. Shallow angle may be at least about 0°, 1°, 2°, 5°, 10°,15°, 20°, 25°, 30°, or 35°. Shallow angle may be at most about 0°, 1°,2°, 5°, 10°, 15°, 20°, 25°, 30°, or 35°. Shallow angle may be any anglebetween the afore-mentioned values (e.g., from about 0° to about 35°,from about 0° to about 10°, from about 10° to about 25°, or from about25° to about 35°) relative to the target surface and/or a (e.g.,average) layering plane of the object. Intermediate angle may be atleast about 25°, 30°, 35°, 40°, 45°, 50°, 55°, or 60° relative to thetarget surface and/or a (e.g., average) layering plane of the object.Intermediate angle may be at most about 25°, 30°, 35°, 40°, 45°, 50°,55°, or 60° relative to the target surface and/or a (e.g., average)layering plane of the object. Intermediate angle may be any anglebetween the afore-mentioned values (e.g., from about 25° to about 60°,from about 25° to about 35°, from about 35° to about 50°, or from about50° to about 60°) relative to the target surface and/or a (e.g.,average) layering plane of the object. Steep angle may be at least about45°, 50°, 55°, 60°, 65°, 70°, 75°, 80°, 85°, or 90° relative to thetarget surface and/or a (e.g., average) layering plane of the object.Steep angle may be at most about 45°, 50°, 55°, 60°, 65°, 70°, 75°, 80°,85°, or 90° relative to the target surface and/or a (e.g., average)layering plane of the object. Steep angle may be any angle between theafbre-mentioned values (e.g., from about 45° to about 90°, from about45° to about 60°, from about 60° to about 75°, or from about 75° toabout 90°) relative to the target surface and/or a (e.g., average)layering plane of the object. The bottom skin layer may comprise a topsurface and a bottom surface. The bottom skin layer may be a wire or aledge or have a planar surface. At least a portion of the first portion(e.g., the top surface of the top layer, 670) and a portion of thesecond portion (e.g., the bottom surface of the bottom skin layer, 672)may be separated by pre-transformed material (e.g., 616). At least aportion of the first portion (e.g., the top surface of the top layer,674) and a portion of the second portion (e.g., the bottom surface ofthe bottom skin layer, 676) may be separated by a gap (e.g., 656). Thegap may be filled with pre-transformed material and may be transformed(e.g., subsequently hardened) during the formation of the 3D object.FIG. 6C shows an example of a portion (e.g., 692) of a 3D object, whichportion comprises a bottom skin layer (e.g., 690), that is not connectedto a rigid-portion. The portion of the 3D object may be formed in amaterial bed (e.g., 680) within an enclosure (e.g., comprising 684). Theportion of the 3D object may comprise one or more layers formed adjacentto (e.g., above) the bottom skin layer (e.g., 686, 688). The bottom skinlayer may be floating (e.g., suspended) anchorlessly within the materialbed. The bottom skin layer and/or the one or more layers adjacent to thebottom skin layer may not be connected to a rigid-portion. The bottomskin layer may be formed using any 3D printing methodologies describedherein.

In some embodiments, the 3D object comprises at least one overhang. Theoverhang of the 3D object may be at least partially defined by theorientation of the 3D object with respect to the target surface (e,g,exposed surface of the material bed and/or the support surface of theplatform) and/or a (e.g., average) layering plane. The overhang of the3D object may be at least partially defined by the orientation of the 3Dobject with respect to the layering plane (e.g., FIG. 47B, 4741), and/ordirection perpendicular to the build direction (e.g., exposed surface ofthe material bed and/or the support surface of the platform) and/or a(e.g., average) layering plane. The build direction may be opposite tothe direction in which the platform is lowered during the printing(e.g., FIG. 1, 112). The build direction may be the direction oflayerwise formation (e.g., direction of deposition one layer on another,e.g., growth direction of the 3D object during its printing). The growthdirection may oppose the direction in which the platform is loweredduring the printing. For example, an overhang portion of a 3D object maybe oriented at shallow, steep and/or intermediate angle with respect tothe target surface, layering plane, and/or the direction perpendicularto the 3D object's growth direction, during printing. FIG. 41A shows aperspective view of an example object 4100 having a toroid shape(including a support member 4101, which may be removed from the object,e.g., after the printing). An overhang can include (e.g., correspond to)a cavity ceiling (e.g., 4102) and/or a cavity bottom (e.g., 4104) of theobject. The overhang (e.g., cavity ceiling and/or cavity bottom) may befree auxiliary supports during the printing. For example, the overhangmay be supported by (e.g., coupled to) a previously transformed (e.g.,hardened) material of the (e.g., requested) object, during the printing.FIG. 41B shows a perspective view of an example object 4120 having animpeller shape (including a support member 4121, which may be removedfrom the 3D object, e.g., after its printing). An overhang can include(e.g., correspond to) a bottom portion (e.g., bottom surface) of a ledge(e.g., 4122) (e.g., blade) of the object. The overhang (e.g., ledge orblade) may be free of auxiliary supports during its printing. Forexample, the overhang may be supported by previously transformed (e.g.,hardened) material of the object and/or the material bed (e.g., powder)during its printing. The overhang may be supported in only one of itssides (e.g., to the core of the impeller 4120) during its printing.Printing process parameters, such as one or more characteristics of theenergy beam(s) (e.g., power/energy, power density at the target surface,dwell time, scan speed, focus, and/or beam width), may be adjusteddepending on whether the overhang being printed is at a shallow, steepor intermediate angle relative to the target surface, layering plane,and/or a direction perpendicular to the direction of build, in order toreduce (e.g., eliminate) deformation of the overhang and/or otherportion of the object. For example, different portions of the object4100 of FIG. 41A and/or the object 4120 of FIG. 41B may be printed usingdifferent energy beam characteristic(s).

In some embodiments, the 3D object is printed using printing processparameters. The printing process parameters may be adjusted dependingwhich part of the overhang is being printed and/or the type of overhang.For example, a skin (e.g., bottom skin) of the overhang may be printedusing one or more different conditions compared to a core portion (alsoreferred to herein as the “core” or “interior portion”) of the overhangand/or 3D object. The bottom skin of the overhang can refer to a portion(e.g., a layer) of the overhang that includes the surface of theoverhang that is most proximate to the support surface of the platform(e.g., bottom-most surface of the overhang). FIG. 42A shows an exampleof a section view of a 3D object 4200, which includes rigid portion(e.g., previously-formed edge of the object) 4202 from which an overhang4204 can be formed. The overhang can include a skin (e.g., bottom skin)(e.g., 4209) and core (e.g., 4208), e.g., deposited on the skin. Theskin (e.g., bottom skin) of the overhang can include an exterior (e.g.,exposed) surface of the overhang. The rigid portion (e.g., 4202) mayinclude a core (also referred to as a rigid portion core) (e.g., 4206)and a skin (also referred to as a rigid portion skin) (e.g., 4203). Theoverhang may attach to the rigid portion. The rigid portion may compriseone or more layers of hardened material. The overhang can include aplurality of layers (e.g., 4205 a, 4205 b, 4205 c, and 4205 d). Eachlayer of the overhang can include portions of the skin (e.g., bottomskin) (e.g., 4209) and core (e.g., 4208). The core can comprise PMX or arigid portion. The exterior surface of the overhang (e.g., bottom skin)may be at an angle (e.g., α) of about 45, 35, 30, 25, 20, 15 or 10degrees or lower with respect to a (e.g., average) layering plane (e.g.,4210), an exposed surface of the material bed and/or a supportingsurface of the build platform. In some embodiments, the skin (e.g.,bottom skin) of the overhang is formed using different processparameters than those for forming the core of the overhang. In someembodiments, the skin (e.g., bottom skin) of the overhang is formedusing the same process parameters as those for the core of the overhang.The overhang can be a ceiling of the 3D object. FIG. 42B shows a sectionview of a 3D object 4220, which includes a ceiling 4224. The ceiling maybe printed from rigid portions (e.g., 4222 a and 4222 b). In someembodiments, the ceiling is formed by sequentially forming ledges untilthe ledges meet to form a bridge. The ceiling may include a skin (e.g.,bottom skin) (e.g., 4226) and a core (e.g., 4227). In some cases, thecore (e.g., 4227) is formed over the bottom skin (e.g., the bottom skinmay support a portion of the core during printing). The rigid portions(e.g., 4222 a and 4222 b) may include a core (also referred to as rigidportion core) (e.g., 4228 a or 4228 b) and a skin (also referred to asrigid portion skin) (e.g., 4230 a or 4230 b). The exterior surface ofthe ceiling (e.g., bottom skin) may be at an angle (e.g., α₁ or α₂) ofabout 45, 35, 30, 25, 20 degrees or lower with respect to a (e.g.,average) layering plane of the object, an exposed surface of thematerial bed and/or a support surface of the build platform. The anglesα₁ or α₂ may be the same or different.

In some cases, different portions of an object are formed usingdifferent processes. For example, an interior portion can be formedusing a different process than a process used to form an overhang and/orskin portion. In some embodiments, different portions of an overhang(and corresponding bottom skins) are formed using differenttransformation processes (e.g., at least partially based on an anglerelative to the layering plane and/or stacking vector). For example, afirst portion of an overhang (and corresponding bottom skin portion) maybe formed using a first transformation process (e.g., MTO, STO and/orPMX), and a second portion of the overhang (and corresponding bottomskin portion) may be formed using a first transformation process (e.g.,MTO, STO and/or PMX) different than the first transformation process.Different processes may result in different portions of the overhangmaterials of different properties (e.g., microstructure, density and/orsurface roughness). For example, a first portion of the overhang (andcorresponding bottom skin) may have a first property, and a secondportion of the overhang (and corresponding bottom skin) may have asecond property that is different than the first property. The propertycan be a material characteristic.

In some embodiments, an object can have at least 2, 3, 4, 5 or moreregions of different material properties (e.g., microstructure, densityand/or surface roughness).

In some embodiments, the 3D object comprises an overhang. The overhangmay at least partly be defined by a stacking vector (e.g., FIGS. 42A or42B, vector “Z”) anchor a layering plane (e.g., FIG. 42A, 4210 or FIG.42B, 4231). FIG. 42C shows an example of a section view of an overhangportion 4230 of a 3D object. The bottom surface of an overhang can havean exterior surface (e.g., 4232), where a vector normal (e.g., V_(a)) tothe exterior surface that is (i) directed into the object and (ii) has apositive projection onto the stacking vector (e.g., “Z”), is at an acuteangle (e.g., alpha (α)) and/or an obtuse angle (beta (β)) with respectto a layering plane (or an average layering plane) (e.g., 4236). Theacute angle (e.g., alpha (α)) and the obtuse angle (e.g., beta (β)) maybe supplementary angles. The acute angle (e.g., alpha (α)) can be atleast about 45 degrees (°), 50°, 55°, 60°, 70°, 80°, or 85°. The acuteangle (e.g., alpha (α)) can be at most about 90 degrees. The obtuseangle (e.g., beta (β)) can be complementary to alpha. FIG. 42D shows anexample of a section view of an overhang portion 4240 of a 3D object. Insome embodiments, a bottom surface of an overhang can have an exteriorsurface (e.g., 4242), where a vector normal (e.g., V_(n)) to theexterior surface that is (i) into the object and (ii) has a positiveprojection onto the stacking vector (e.g., “Z”), is at an acute angle (eg , gamma (γ)) and/or an obtuse angle (e.g., delta (67 )) with respectto the stacking vector (e.g., “Z”). The acute angle (e.g., gamma (γ))and the obtuse angle (e.g., delta (δ)) may be supplementary angles. Theacute angle (e.g., gamma (γ)) can be at most about 45°, 40°, 35°, 30°,25°, 20°, 15°, 10°, 5°, or 1°, The obtuse angle (e.g., delta (δ)) can bethe supplementary angle to gamma.

In some instances, it is desirable to control the manner of forming atleast a portion of a layer of hardened material (e.g., core and/oroverhang). The layer of hardened material may comprise a plurality ofmelt pools. The FLS (e.g., depth, or diameter) of the melt pool may beat least about 0.5 μm, 1 μm, 5 μm, 10 μm, 20 μm, 30 μm, 40 μm, 50 μm, 60μm, 70 μm, 80 μm, or 100 μm. The FLS of the melt pool may be at mostabout 0.5 μm, 1 μm, 5 μm, 10 μm, 20 μm, 30 μm, 40 μm, 50 μm, 60 μm, 70μm, 80 μm, or 100 μm. The FLS of the melt pool may be any value betweenthe afore-mentioned values (e.g., from about 0.5 μm to about 100 μm,from about 0.5 μm to about 10 μm, from about 10 μm to about 30 μm , fromabout 30 μm to about 50 μm, or from about 50 μm to about 100 μm).

In some instances, it is desired (e.g., requested) to control one ormore characteristics of the fabricated 3D object (e.g., or portionsthereof). For example, it may be desirable to control the manner offorming and/or hardening an overhang (e.g., a hanging structure (e.g.,ceiling of a cavity or ledge)) as part of the 3D object. The 3D printingmethodologies (e.g., methods, apparatuses, systems, and/or software)described herein may utilize a type-2 energy beam and/or a type-1 energybeam (collectively referred to herein as “transforming energy” or“transforming energy beam”). The type-2 energy beam and the type-1energy beam may differ by at least one characteristic of the irradiatingenergy. For example, the type-2 energy beam and the type-1 energy beammay differ in their cross section (e.g., with the type-2 energy beamhaving a larger cross section than the type-1 energy beam). For example,the type-2 energy beam and the type-1 energy beam may differ in theirpower density (e.g., with the type-2 energy beam having a lower powerdensity than the type-1 energy beam). For example, the type-2 energybeam and the type-1 energy beam may differ in their focus (e.g., withthe hatching energy source being more focused than the type-2 energybeam). For example, the type-2 energy beam and the type-1 energy beammay differ in their path trajectory while generating (e.g., directly, orindirectly) a layer of hardened material (e.g., with the type-2 energybeam traveling along the path of tile trajectory, whereas the type-1energy beam hatches along another trajectory). For example, the type-2energy beam and the type-1 energy beam may differ in their manner ofmovement while transforming a layer when forming, a 3D object (e.g., atype-2 energy beam may be (e.g., substantially) stationary for a periodof time, whereas the type-1 energy beam may be constantly moving). Insome embodiments, at least one characteristic (e.g., cross sectionand/or power density) of the energy beam is modified during part or allof the transformation (e.g., melting) process. In some embodiments, thefocus of the energy beam is modified during part or all of thetransformation (e.g., melting) process. For example, the energy beam canbe focused for part of the transformation and defocused during anotherpart of the transformation.

In some embodiments, hatching and/or tilting energy beams are used toform different portions of a 3D object. Various 3D objects and portionsthereof (e.g., including a rim), apparatuses (e.g., controllers),systems (e.g., 3D printers), software, methods related to the formationof these 3D objects (e.g., generated using tiling and/or hatching), aswell as various control schemes are described in U.S. patent applicationSer. No. 15/435,128, PCT patent application number PCT/US/17/18191, orEuropean patent application number EP17156707.6, each of which isincorporated herein by reference in its entirety wherenon-contradictory.

The use of a type-1 energy beam or type-2 energy beam may depend, inpart, on the geometry of the 3D object. For example, a type-1 energybeam can be used to form a contour (which can be referred to as a rim,skin (e.g., thickness of the skin), or perimeter portion) of a 3Dobject. For example, a type-2 energy beam can be used to form aninterior portion (also referred to as “core”) of the 3D object. In somecases, the bulk of the interior portion has a FLS (e.g., width, lengthor height) that is larger than the FLS (e.g., width, length or height)of a tile. The FLS may be a horizontal FLS (e.g., width or length). Forexample, a type-1 energy beam can be used to form a narrow portion ofthe interior of the 3D object (e.g., having a horizontal FLS that issmaller than the FLS of the tile). To illustrate, FIGS. 28A-28D showexamples of top views of 3D objects each having at least one layer ofhardened material illustrating various path trajectories of the energybeams used in the formation of a layer of hardened material. FIG. 28Ashows an example portion 2810 of a 3D object having a contour 2811 withhatches 2812 made by a type-1 energy beam. The hatches (e.g., 2812) canbe made prior to forming a path-of-tiles (not shown). FIG. 28B shows anexample of a portion 2820 of the 3D object having, a contour 2821 withhatches 2822 made by a type-1 energy beam, and an interior having tiles2823 made by a type-2 energy beam. FIG. 28C shows an example where aportion 2830 of a 3D object with an interior having tiles 2832 made by atype-2 energy beam prior to forming hatches to fill in narrow section2833. The contour (e.g., 2831) can be formed before, after, orsimultaneously with the tiles (e.g., 2832). The hatches (e.g., 2822) canbe formed before, after, or simultaneously with forming the tiles (e.g.,2823). FIG. 28D shows a portion 2840 of a 3D object having contour 2841with hatches 2842 (e.g., both made by a type-1 energy beam), an interiorhaving tiles 2843 made by a type-2 energy beam and redacted tiles 2844.Redacted tiles 2844 can be formed using the type-2 energy beam, e.g.,that is masked (e.g., using a mask or a restrictive aperture).

In some embodiments, a contour (rim) of a at least a portion of a 3Dobject is processed using a tiling methodology (e.g., that uses acontinuous or pulsing energy beam, e.g., that uses a type-1 energy beamor type-2 energy beam as disclosed herein). For example, a contour (rim)of a at least a portion of a 3D object can be generated using a type-2energy beam. In some cases, this can result in the at least the portionof the 3D object having a smooth surface finish having low Ra or Savalue, and/or having high specular reflectivity). The high specularreflectivity of a surface of the at least the portion of the 3D objectmay be at least about 2%, 5%, 15%, 25%, 35%, 45%, 55%, 65%, 70%, or 80%.The high specular reflectivity of a surface of the at least the portionof the 3D object may be of any value between the afore mentioned values(e.g., front about 2% to about 80%, front about 2% to about 25%, frontabout 15% to about 45% or from about 35% to about 80%). The high surfacereflectivity and/or low roughness of the at least a portion of the 3Dobject surface may allow visualization of a tessellation present in themodel and/or printing instructions used to generate the 3D object, e.g.,when that surface comprises a curvature.

FIGS. 36A-36D show examples of horizontal (e.g., top or bottom) views of3D objects each having at least one layer of hardened materialillustrating various path trajectories of the energy beams used in theformation of hardened material, in accordance with some embodiments. Therim and the interior of a layer of hardened material may be generatedusing the same energy beam, or different energy beams. The tiles and theinterior may be formed with the same or with different transformationmethodology (e.g., tiling or hatching methodology), At least one of therim and the interior of a layer of hardened material may be generated bya combination of different transformation methodology (e.g., tilingmethodology or hatching methodology). The tiles may be of any shape(e.g., corresponding to the shape of the energy beam cross section orfootprint on the target surface. For example, the tiles may beelliptical (e.g., round), as shown in the example of FIG. 36C, 3632. Forexample, the tiles may be rectangular (e.g., square), as shown in theexample of FIG. 36B, 3622. In some examples, the rim may be formed usinga combination of type-2 energy beam and type-1 energy beam. FIG. 36Ashows an example of a layer of a 3D object 3610 having a rim comprisingtiles 3611 and 3612 formed using a tiling methodology (e.g., step andrepeat) with a type-2 energy beam (that generates circular tiles); andan interior 3615 made using a hatching methodology using the type-1energy beam. In some cases, at least two of the tiles (e.g., FIG. 36A,3612) that are adjacent to each other in a path of tiles, overlap witheach other. In some cases, at least two of the tiles in a path of tilesdo not overlap (not shown). For example, at least two of the tiles inthe path of tiles may contact or not contact each other. The tiles(e.g., FIG. 36A, 3612) of the rim (e.g., a perimeter, contour, or outersurface of a layer) can be made prior to, simultaneously with, or afterforming an interior portion 3615. The tiles and the interior can beformed using any suitable energy beam (e.g., a type-1 energy beam, or atype-2 energy beam). FIG. 36B shows an example of a layer of a 3D object3620 having a rim comprising tiles 3621 and 3622, and an interiorportion comprising tile 3625 generated by the tiling methodology using atype-2 energy beam (that generated rectangular tiles). FIG. 36C shows anexample where a 3D object layer 3630 has a rim comprising tiles 3631 and3632 formed using a tiling methodology with an interior portion 3635that is free of hardened material. That is, interior portion 3635 cancorrespond to a voided region that is surrounded by (e.g., defined by)the rim comprising tiles 3631 and 3632. FIG. 36D shows a layer 3640 of a3D object having a rim comprising tiles 3641 and 3642 generated using amethodology with a type-2 energy beam, an interior portion comprising(i) overlapping tiles comprising tile 3645 made by a tiling methodologyusing the type-2 energy beam, and (ii) hatches 3646 (e.g., in areas thatare too narrow to form tiles) generated by the hatching methodologyusing the type-1 energy beam.

In some cases, the tiles create a repetitive microtexture on an exteriorsurface of the 3D object. The exterior surface may be an exteriorsurface of a skin of the 3D object. The repetitive microtexture may beat least in a localized surface area of the 3D object. The repetitivemicrotexture may correspond to scales (e.g., FIG. 57A). The repetitivemicrotexture may correspond to tiles (e.g., overlapping tiles). Therepetitive microtexture may have crescent shapes. The repetitivemicrotexture may be periodic. The repetitive microtexture may becharacterized by a profile of the exterior surface (or a portion of theexterior surface). FIG. 51B shows an example microtexture (profile) ofan exterior surface 5120 of a layer of a 3D object (e.g., FIG. 36D,cross-section A-A), showing an intralayer periodic repetitivemicrotexture. FIG. 51C shows an example profile of an exterior surface5140 across multiple layers 5141, 5143 and 5145 of a 3D object, showingan interlayer periodic repetitive microtexture. The exterior surface canhave regions of relative depression (e.g., FIG. 51B, 5122 or FIG. 51C,5142) and regions of relative elevation (e.g., FIG. 51B, 5124 or FIG.51C, 5144). The regions of relative elevation may be referred to aspeaks. The regions of relative depression may be referred to as valleys.The peaks and valleys may be an alternating series of peaks and valleys.A profile across multiple layers (interlayer microtexture) may be (e.g.,substantially) flat or may have different elevations (e.g., 5141, 5143and 5145) (e.g., with respect to the platform). The profile across themultiple layers (interlayer microtexture) may be stepped (e.g., eachstep corresponding to a layer). The profile across the multiple layers(interlayer microtexture) may be in accordance with a slope line (e.g.,5147) with respect to a layering plane defined by at least one layer.The interlayer and intralayer microtexture can form a two-dimensionalarray of periodic peaks and valleys corresponding to a scaled surfacetexture (e.g., FIG. 57A). The valleys (e.g., FIG. 51B, 5122 or FIG. 51C,5142) can correspond to overlapping regions of tiles. The peaks (e.g.,FIG. 51B, 5124 or FIG. 51C, 5144) may have curved (e.g., rounded)exterior surface in accordance with a melting and/or solidification ofthe material as a result of the transforming. The peaks may besymmetrically rounded or non-symmetrically rounded (e.g., lopsided). Thedepths (e.g., FIG. 51B, 5122 or FIG. 51C, 5142) of the valleys may vary.In some embodiments, a depth of at least one of the valleys (or anaverage depth of a number of valleys) is at most about 0.5 micrometers(μm), 1 μm, 2 μm, 3 μm, 4 μm, 5 μm, 10 μm, 15 μm, 20 μm, 30 μm, 40 μm,or 50 μm. The depth of at least one of the valleys (or an average depthof a number of valleys) can range between any of the aforementionedvalues (e.g., from about 0.5 μm to 50 μm, from about 0.5 μm to 20 μm,from about 20 μm to 50 μm, or from about 2 μm to 20 μm). The distance(e.g., FIG. 51B, 5123 or FIG. 51C, 5149) between the valleys maycorrespond to distances between tiles (e.g., between overlappingportions of the tiles). In some embodiments, the distance between thevalleys is (e.g., substantially) the same as the distance betweencenters of the tiles. In some, embodiments, the distance (e.g., FIG.51B, 5123) between at least two successive valleys within an intralayermicrotexture is at least about 10 micrometers (μm), 15 μm, 20 μm, 25 μm,30 μm, or 35 μm, 50 μm, 70 μm, 80 μm, 100 μm, 200 μm, 250 μm, 300 82 m,350 μm, 400 μm, 450 μm or 500 μm. In some embodiments, the distance(e.g., FIG. 51C, 5149) between at least two successive valleys of aninterlayer microtexture is at least about 50 millimeters (mm), 100 mm,150 mm, 200 mm, 300 mm, 400 mm or 500 mm. In some embodiments, distances(e.g., FIG. 51B, 5123) between valleys of an intralayer microstructure(e.g., FIG. 51B) is more consistent than distances (e.g., FIG. 51C,5129) between valleys of an interlayer microstructure (e.g., FIG. 51C).The peaks may be curved (e.g., rounded) in accordance with a hardening(e.g., solidification) of the pre-transformed material as a result ofits transformation (e.g., melting). The peaks may be symmetricallyrounded or non-symmetrically rounded (e.g., lopsided).

It should be noted that any suitable combination of energy beams (e.g.,type-2 energy beam and type-2 energy beam) can be used to form anysuitable portion (e.g., contour and interior portion) of a 3D object,and that the embodiments shown in FIGS. 28A-28D and 36A-36D are notmeant to be exhaustive of all suitable embodiments described herein Thatis, the tiles can have any suitable shape and size, and can be (at leastin part) overlapping or non-overlapping in the contour and/or theinterior portion of a 3D object. The path of tiles can be in accordancewith a substantially straight line or in accordance with the curvedline. The tiles in the contour and/or the interior portion of the 3Dobject may be redacted tiles (e.g., that are masked (e.g., using a maskor a restrictive aperture)), as described herein. In some embodiments,at least three of the tiles in a path of tiles are uniformly spacedapart from each other (e.g., distances between centers or edges of thetiles are substantially the same). In some embodiments, at least threeof the tiles in a path of tiles are non-uniformly spaced apart from eachother (e.g., distances between centers or edges of the tiles are notsubstantially the same). The dimensions of at least two of the tileswithin a path of tiles (and/or within a given layer) can have (e.g.,substantially) the same size or have different sizes. The size of eachtile can correspond with the size of each melt pool that makes up eachtile. For example, FIGS. 37A and 37B show schematic horizontal viewexamples of overlapping tiles and non-overlapping tiles, in accordancewith some embodiments. FIG. 37A shows an example of a cross-section viewof a portion of a path 3700 comprising circular-shaped tiles 3702 havingthe same size (e.g., have the same diameter 3704) and spaced apart fromeach other a uniform distance 3706 (as measured from adjacent centers oftiles 3702). In the example shown in FIG. 37A, tiles 3702 overlap witheach other in that they are spaced apart by distance 3706 that is lessthan diameter 3704. In some embodiments, a distance between the tilecenters (e.g., FIG. 37A, 3706) is at least about 0.9, 0.75, 0.6, 0.5,0.25, or 0.01 of a diameter of a horizontal cross section of the exposedsurface of the tiles (e.g., FIG. 37A, 3704). In some embodiments, thedistance between the tile centers ranges between any suitable rangesdescribed above (e.g., from about 0.5 to about 0.75, from about 0.25 toabout 0.75, or from about 0.5 to about 0.6) of the diameter of ahorizontal cross section of the exposed surface of the tiles). In someembodiments, a distance between tile centers of at least two ofsuccessive tiles is at least about 10 micrometers (μm), 15 μm, 20 μm, 25μm, 30 μm, or 35 μm, 50 μm, 70 μm, 80 μm, 100 μm, 200 μm, 250 μm, 300μm, 350 μm, 400 μm, 450 μm or 500 μm. In some embodiments, the distancebetween the tile centers is at most about 50 millimeters (mm), 100 mm,150 mm, 200 mm, 300 ram, 400 mm or 500 mm. In some embodiments, thedistance between the tile centers ranges between any of theaforementioned values (e.g., from about 10 μm to about 500 mm, fromabout 10 μm to about 500 μm, from about 500 μm to about 500 mm, or fromabout 15 μm to about 30 μm). FIG. 37B shows an example of across-sectional view of a portion of a path 3720 comprisingcircular-shaped tiles 3722 having the same size (e.g., have the samediameter 3724) that are spaced apart from each other by a uniformdistance 3726 (e.g., as measured from adjacent centers of tiles 3722).In the example shown in FIG. 37B, tiles 3722 do not overlap as they arespaced apart by distance 3726 that is the same as (e.g., or can begreater than in other examples) diameter 3724. In some embodiments, atleast a rim of a portion of a layer of hardened material comprises tileshaving cross sectional diameters (e.g., FIG. 37A, 3704 or FIG. 7B, 3724)having a fundamental length scale (FLS) of any of the type-2 energybeams described herein.

FIGS. 38A and 38B show images of example various 3D objects having rimsformed using a tiling process as described herein. FIG. 38A shows a topview example of 3D object 3800 (marked “11”), which includes contour3802 having a number of overlapping tiles 3804 that are (e.g.,substantially) uniformly spaced apart from each other. In someembodiments, the external contour (also referred herein as “rim”, e.g.,3804) may form the skin (also referred herein as the “exterior portion”or “outer portion”) of the object. An example of the skin (formed of aplurality of contours) is depicted in FIG. 38B, 3829. In someembodiments, the rim (e.g., FIG. 38A, 3802, also referred to as acontour, or contour portion) has a thickness (e.g., FIG. 38A, 3806) thatcorresponds to the FLS of the energy beam forming the rim (e.g., thetype-1 energy beam or the type-2 energy beam, e.g., as describedherein). The FLS can be a diameter or diameter equivalent of an exposedsurface of the tile. In some embodiments, the tiles (e.g., FIG. 38A,3804) are space a substantially uniform distance (e.g., FIG. 38A, 3808)from each other (as measured from center of adjacent tiles. e.g., 3804shown in the example of FIG. 38A) that corresponds to the percentage ofoverlapped area (e.g., pertaining to the tiles) as disclosed herein.Adjacent tiles may be separated from each other by tile boundaries,which may be visible, e.g., as small surface borders (e.g.,indentations) between the tiles centers. An interior portion can beformed using any of the transformation processes described herein. FIG.38A shows an example of an interior portion 3810 made of hatches. Insome embodiments, interior portion is formed using a type-1 energy beam,in accordance with some embodiments described herein. FIG. 38B shows anexample of a top view of 3D object 3820 (marked “8”), which includes rim3822 comprised of several overlapping tiles 3824 that are (e.g.,substantially) uniformly spaced apart from each other. In the exampleshown in FIG. 38B, rim 3822 has a thickness that corresponds to the FLSof the type-2 energy beam that generated the rim. In the example shownin FIG. 38B, tiles 3824 are spaced a (e.g., substantially) uniformdistance 3828 from each other (as measured from center of adjacent tiles3824). In the example shown in FIG. 38B, the interior portion 3827 isformed using a hatching transformation methodology using a type-1 energybeam. The 3D object 3820 shown in the example of FIG. 38B, indicates anexterior surface 3829 (also referred to as an outer surface, externalsurface, or exposed surface) that has a high specular reflection and lowroughness.

In some embodiments, the 3D object formed by one or more methodsdescribed herein comprises a high specular reflectivity (e.g., at awavelength range and an angle of incidence). Formation of a 3D object byat least one methodology described herein may result in a 3D objecthaving at least one surface which is characterized by a specularreflectance percentage (e.g., at a wavelength range and an angle). Thespecular reflectance percentage may be of at least about 2%, 5%, 10%,15%, 20%, 30%, 40%, 50%, 60%, or 75%. The specular reflectancepercentage may be of any value between the afore-mentioned values (e.g.,from about 2% to about 70%, from about 2%, to about 20%, from about 10%to about 40%, from about 30% to about 75%). The wavelength range may bethe visible wavelength range (e.g., visible to an average human eye).The angle may be normal incidence to the surface. The specularreflectance percentage (%R) at an angle of incidence and a wavelengthrange is one hundred (100) times the ratio of: (i) specular reflectance(R_(Specular)) at that angle of incidence and at that wavelength rangeover (ii) total reflectance (R_(Total)) at that angle of incidence andat that wavelength range, from a surface (e.g., in a formula format:%R=100*R_(Specular)/R_(Total)). For example, the values of specularreflectance percentage can be at normal incidence to the surface andover the visible wavelength range.

In some embodiments, an exterior surface of the 3D object (e.g., thatcomprises a rim portion formed using a tiling process) is characterizedas having a Sa value of at most about 60 μm, 50 μm, 40 μm, 20 μm, 10 μm,9.5 μm, 9 μm, 8.5 μm, 8 μm, 7.5 μm, 7 μm, 6.5 μm, 6 μm, 5.5 μm, 5 μm,4.5 μm, 4 μm, 3.5 μm, 3 μm, 2 μm, or 1 μm. In some embodiments, theexternal surface (e.g., exterior surface 3829) has a Sa ranging betweenany of the values listed above (e.g., from about 60 μm to about 1 μm,from about 10 to about 1 from about 5 μm to about 1 μm, or from about 3μm to about 1 μm). It should be noted that the 3D objects represented inFIGS. 38A and 38B are shown as examples and do not limit the scope(e.g., dimensions, properties, etc.) of other 3D objects formed usingany of the processes described herein. As illustrated in the example 3Dobjects in FIGS. 38A and 38B, tiles (e.g., 3804 and 3824) can be visiblydistinct portions of hardened material (e.g. solid metal) that aredefined by edges and middle portions. The visibly distinct is by a nakedeye or using a magnification (e.g., optical microscopy or a magnifyingglass). These distinct edges and middle portions can be a product of thetransformation (e.g., melting) and/or hardening (e.g., by cooling)process of each melt pool formed during a transformation process (e.g.,using a tiling process). The tile can reflect light differently oncehardened (e.g., as opposed to being transformed and/or pre-transformed).The hardened tiles may be visibly different from transformed portionand/or pre-transformed material. Visibly different may comprise havingdifferent (e.g., specular) reflectivity. In some embodiments, the edgesand/or middle portions may comprise microstructures that differ in atleast one microstructure characteristics. The microstructurecharacteristics may comprise microstructure type, material composition,grain orientation, material density, degree of element segregation (orof compound segregation) to grain boundaries, material phase,metallurgical phase, crystal phase, crystal structure, materialporosity, or any combination thereof. The microstructure type maycomprise a metallurgical phase anchor morphology. The microstructuretype may comprise a crystallographic phase and/or crystal morphology.The microtexture type may comprise planar structure, cellular structure,columnar dendritic structure, or equiaxed dendritic structure. A crosssection (e.g., vertical cross section) of the generated (i.e., formed)3D object may reveal a microstructure (e.g., grain structure) indicativeof a layered deposition and/or melt pool formation. Without wishing tobe bound to theory, the microstructure (e.g., grain structure) may arisedue to the solidification of transformed (e.g., powder) material that istypical to and/or indicative of a particular 3D printing method. Forexample, a cross section may reveal a microstructure indicative ofsolidified melt pools that are formed in a 3D printing process, e.g., asdescribed herein (e.g., and are indicative of this process). The crosssection of the 3D object may reveal a substantially repetitivemicrostructure (e.g., grain structure). The microstructure (e.g., grainstructure) may comprise substantially repetitive variations in materialcomposition, grain orientation, material density, degree of compoundsegregation or of element segregation to grain boundaries, materialphase, metallurgical phase, crystal phase, crystal structure, materialporosity, or any combination thereof. The microstructure (e.g., grainstructure) may comprise substantially repetitive solidification oflayered melt pools. The melt pool may have an average FLS of at leastabout 0.5 μm, 1 μm, 5 μm, 7 μm, 20 μm, 30 μm, 40 μm, 50 μm, 60 μm, 70μm, 80 μm, 90 μm, 100 μm, 150 μm, 200 μm, 250 μm, 300 μm, 350 μm, 400μm, 450 μm, 500 μm, or 1000 μm. The substantially repetitivemicrostructure may have an average height of at most about 1000 μm, 500μm, 450 μm, 400 μm, 350 μm, 300 μm, 250 μm, 200 μm, 150 μm, 100 μm, 90μm, 80 μm, 70 μm, 60 μm, 50 μm, 40 μm, 30 μm, 20 μm, or 10 μm. The meltpool may have an average FLS of any value between the afore-mentionedvalues (e.g., from about 0.5 μm to about 1000 μm, from about 15 μm toabout 50 μm, from about 5 μm to about 150 μm, from about 20 μm to about100 μm, or from about 10 μm, to about 80 μm). The melt pool FLS maycorrespond to the height of a layer of hardened material. The FLS of themelt pool may comprise a height of the melt pool, a diameter (ordiameter equivalent) of an exposed surface of the melt pool, or a radius(or radius equivalent) of an exposed surface of the melt pool,

In some examples, the microstructures (e.g., of melt pools) are measured(and examined) by a microscopy method. The microscopy method maycomprise ultrasound or nuclear magnetic resonance. The microscopy methodmay comprise optical microscopy. The microscopy method may compriseelectromagnetic, electron, or proximal probe microscopy. The electronmicroscopy may comprise scanning, tunneling, X-ray photo-, or Augerelectron microscopy. The electromagnetic microscopy may compriseconfocal, stereoscope, or compound microscopy. The microscopy method maycomprise an inverted and/or non-inverted microscope. The proximal probemicroscopy may comprise atomic force, or scanning tunneling microscopy,or any other microscopy described herein. The microscopy measurementsmay comprise using an image analysis system. The microstructures may bemeasured by a contact or by a non-contact method. The microstructuresmay be measured by using an electromagnetic beam (e.g., visible or IR).The microstructure measurements may comprise evaluating the dendriticarm spacing and/or the secondary dendritic arm spacing (e.g., usingmicroscopy). The microscopy measurements may comprise an image analysissystem. The measurements may be conducted at ambient temperatures (e.g.,R.T.), melting point temperature (e.g., of the powder material) orcryogenic temperatures.

Thus, the path of tiles (e.g., formed by sequential tiles) may fill thetarget layer of hardened material (e.g., corresponding to a target sliceof the 3D object model). In some examples, the type-2 energy beam andthe type-1 energy beam may differ in the portions of transformed and/orhardened material they generate on forming a layer of transformed and/orhardened material as part of the 3D object (e.g., with the type-2 energybeam forming a first portion of transformed material, whereas the type-1energy beam forms a second portion of transformed material. The firstand second portions may or may not directly contact each other oroverlap with each other). In some cases, the type-2 energy beam and thetype-1 energy beam have at least one energy characteristic that is(e.g., substantially) identical. For example, both the type-2 energybeam and the type-1 energy beam may be focused. For example, both thetype-2 energy beam and the type-1 energy beam may be of the same wavelength. For example, both the type-2 energy beam and the hatching energymay be collimated. The type-2 energy beam and type-1 energy beam may begenerated by the same (e.g., type of) energy source, or by differentenergy sources. The type-2 energy beam and type-1 energy beam may bedirected by the same (e.g., type of) scanner, or to different scanners(e.g., FIG. 1, 114 and 120). The type-2 energy beam and type-1 energybeam may travel through by the same (e.g., type of) optical window, orthrough different optical windows (e.g., 115, and 135) on their way to atarget surface.

In another aspect, a 3D object comprises successive regions of hardenedmaterial indicative of at least one additive manufacturing process. Forexample, the hardened material may comprise melt pools. An average FLSof the melt pools in a first portion of the 3D object may be larger thanthe average FLS of the melt pools in a second portion of the 3D object.For example, the average FLS of the melt pools in a surface of the 3Dobject may be larger than the average FLS of the melt pools in theinterior of the 3D object. The first layer of hardened material may be afirst hardened layer in the object (e.g., bottom skin layer) asindicated by the spatial orientation of the melt pools (e.g., elongatedmelt pools, dripping melt pools, and/or stalactite-like melt pools). Theaverage FLS of the melt pools in the surface can be larger than theaverage FLS of the melt pools in the interior (e.g., by a factor ofabout two or more).

In some embodiments, the porous matrix structure is suspendedanchorlessly in the material bed. In some embodiments, the porous matrixstructure is anchored to the material bed by one or more auxiliarysupport features. The porous matrix structure may or may not be anchoredto the enclosure (e.g., platform). FIG. 8A shows an example of a firstporous matrix 802 and a second porous matrix 804, both disposed in amaterial bed 800 that comprises a pre-transformed (e.g., particulate)material disposed in an enclosure above a platform 801, which materialbed comprises an exposed surface 805. In the example shown in FIG. 8A,the porous matrixes 802 and 804 are suspended anchorlessly in thematerial bed 800. The porous matrixes (e.g., 802 and/or 804) maycomprise a random, irregular, or regular shape. The pores in the porousmatrix structure may comprise a random, irregular, or regular shape. Thehardened material in the porous matrix structure may comprise a random,irregular, or regular shape. The porous matrix may be formed by randomlytransforming the pre-transformed material. The porous matrix may beformed by generating pre-designed structures (e.g., that are not random)by transforming the pre-transformed material. The regular shape maycomprise a geometric shape (e.g., a lattice structure). The porousmatrix may assume an overall irregular, or regular (e.g., cuboid) shape.At times, a first portion of the porous matrix comprises a firststructure, and a second portion of the porous matrix comprises a secondstructure. The first structure may be (e.g., substantially) similar tothe second structure. The first structure may be different from thesecond structure. In some embodiments, the porous matrix comprises alattice. The porous matrix may comprise a random structure. The porousmatrix may comprise a directional structure (e.g., that may direct aflow of transformed material in a certain direction, e.g., channels).FIG. 20B shows examples of various porous matrix structures. Forexample, 2025 shows an example of a honeycomb structure, 2024 shows anexample of a mesh structure, 2023 shows an example of a brick likestructure, 2021, 2022 are examples of random structures of variousdensity. The porous matrix can comprise a space filling polyhedron(e.g., honeycomb pattern). The porous matrix may comprise a latticepattern. The lattice can be a diamond, tetragonal lattice, or cubiclattice. The porous matrix may comprise fibers. The porous matrix callcomprise interconnected features.

In some embodiments, the porous matrix comprises one or more cavities.The cavities may be hollow. The cavities may be devoid, of theparticulate, transformed, and/or hardened material. The cavities maycomprise one or more gasses. The cavities may have cross-sections thatare circular, triangular, square, rectangular, pentagonal, hexagonal, orpartial shapes and/or combinations thereof. The cavity and/or cavitywalls may have a 3D shape. The multiplicity of cavity walls may form theporous matrix structure. The 3D shape of the cavity and/or cavity wallsmay comprise a cuboid (e.g., cube), or a tetrahedron. The 3D shape ofthe cavity may comprise a polyhedron (e.g., primary parallelohedron).The cavity and/or cavity walls may comprise a space-filling polyhedron(e.g., plesiohedron). The polyhedron may be a prism (e.g., hexagonalprism), or octahedron (e.g., truncated octahedron). The cavity and/orcavity walls may comprise a Platonic solid. The cavity and/or cavitywalls may comprise a combination of tetrahedra and octahedra (e.g., thatfill a space). The cavity and/or cavity walls may comprise octahedra,truncated octahedron, and cubes, (e.g., combined in the ratio 1:1:3).The cavity and/or cavity walls may comprise tetrahedra and/or truncatedtetrahedra. The cavity and/or cavity walls may comprise convex polyhedra(e.g., with regular faces). For example, the cavity and/or cavity wallsmay comprise a triangular prism, hexagonal prism, cube, truncatedoctahedron, or gyrobifastigium. The cavity and/or cavity walls maycomprise a non-self-intersecting quadrilateral prism. The cavity and/orcavity walls may comprise space-filling polyhedra. The cavity and/orcavity walls may exclude a pentagonal pyramid. The cavity and/or cavitywalls may comprise 11-hedra, dodecahedra, 13-hedra, 14-hedra, 15-hedra,16-hedron 17-hedra, 18-hedron, icosahedra, 21-hedra, 22-hedra, 23-hedra,24-hedron, or 26-hedron. The cavity and/or cavity walls may comprise atleast 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21,22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39,or 40 faces. The cavity and/or cavity walls may comprise at most 4, 5,6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24,25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, or 40 faces.The cavity and/or cavity walls may comprise any suitable number of facesbetween the afore-mentioned number of faces (e.g., from 4 to 38, from 4to 20, from 20 to 40, or from 10 to 30 faces). The cavity and/or cavitywalls may comprise a non-convex aperiodic polyhedron, convex polyhedron(e.g., Schmitt-Conway bi-prism). The cross-section of the cavity and/orcavity walls (e.g., vertical, or horizontal) may be a square, rectangle,triangle, pentagon, hexagon, heptagon, octagon, nonagon, octagon,circle, or icosahedron. The cavity may be hollow. The cavity walls maycomprise a particulate material (e.g., that was not transformed). Thecavity walls may be composed of a transformed (e.g., and subsequentlyhardened) material. The cavity walls may comprise a material with highporosity. The cavity walls may comprise at least about 30%, 40%, 50%,60%, 70%, 80%, 90% or 95% material, The cavity walls may comprise atmost about 100%, 99%, 95%, 90%, 80%, 70%, 60%, or 50% material. Thecavity walls may comprise a percentage of material corresponding to anypercentage between the afore-mentioned percentages of material (e.g.,the percent may be from 40% to 80%, from 50% to 99%, from 30% to 90%, orfrom 7% to 100% material). The cavity walls may comprise pores. Thelayer of hardened material that is included in the 3D object maycomprise a percentage of material having a value equal to theabovementioned percentages of material of the cavity walls. At least twoof the cavities or cavity walls may have a substantially identical shapeand/or cross section. At least two of the cavities or cavity walls mayhave a different shape and/or cross section. The cavity and/or cavitywalls may be of substantially identical shape and/or cross section. Thecavities and/or cavity walls can be aligned with one another.Alternatively, or additionally, cavities and/or cavity walls can heangularly disposed in relation to one another.

In some embodiments, the porous matrix structure is characterized ashaving a microstructure. The porous matrix may assume at least a portionof the 3D object (e.g., the, entire 3D object). For example, the porousmatrix may assume at least a portion of an overhang as part of the 3Dobject. For example, the porous matrix may assume the entire structureof the 3D object. For example, the porous matrix may assume discreteand/or repetitive portions in a (e.g., forming) 3D object.

In some embodiments, the porous matrix structure is of a (e.g.,substantially) homogenous structure that comprises a plurality of PMXlayers, At times, the porous matrix may be of a heterogeneous structure.FIG. 8B shows an example of a heterogeneous structure. The heterogeneousstructure may be disposed in an enclosure 851, which comprises anexposed surface 855. In the example shown in FIG. 8B, the PMX layers810, 812, 814, 816, 818 and 820 are disposed on a platform 851. Thefirst PMX layer 810 may have a regular shape (e.g., a honeycombstructure). The second PMX layer 812 disposed over the first PMX layermay have a lower porosity structure than the first PMX layer 810. Atleast one of the subsequent fourth, fifth and sixth PMX layers (e.g.,820, 818, 816, respectively) may have a different or similar structureand/or porosity percentage than at least one of the first, second and/orthe third layer. For example, the fourth PMX layer may be denser thanthe second PMX layer, but less dense than the first PMX layer. The fifthPMX layer may have a porosity that is higher than the second PMX layerand/or less than the first or fourth PMX layer. For example, at leasttwo different portions of the porous matrix may be of differentstructures (e.g., microstructure). At least a portion of the porousmatrix layer may comprise a directional structure. The directionalstructure may direct the flow of a flowable (e.g., molten) material, forexample, by forming barriers to restrain and/or direct the flow of theflowable material within the structure. The flowable material maycomprise liquid, semi-liquid, or powder material. For example, theflowable material may comprise molten material. The directionality maycontribute to the formation of a 3D object. The directionality mayaffect the density and/or microstructure in at least a portion of the 3Dobject (e.g., to which the structure is directed towards). Thedirectionality may affect the microstructure of the portion of hardenedmaterial that is (e.g., subsequently) formed at least because of theflow.

In some embodiments, during the process of forming the at least one 3Dobject, a first porous matrix may he separated by one or more layers ofpre-transformed material from another (e.g., a second) porous matrix,thus forming a porous matrix set. FIG. 8A shows an example of a porousmatrix set comprising a first porous matrix 802 and a second porousmatrix 804 separated by a layer of pre-transformed material 803. Porousmatrixes separated by layer(s) of pre-transformed material can bereferred to as porous matrix (PMX) sandwich structures. The porousmatrix set may comprise one or mote porous matrix layers, wherein atleast two of the one or more porous layers ate connected in at least oneposition. The porous matrix set may comprise one or mote porous layers,wherein at least two of the one or more porous layers are disconnected(e.g., separated by one or more layers of pre-transformed material). Theporous matrix set may assume a sandwich like structure which maycomprise two or more porous matrix structures and one or more layers ofpre-transformed (e g., particulate) material disposed between two porousmatrix structures,

At times, the 3D object is formed from a plurality of (e.g., connectedor disconnected) porous matrixes. In some instances, at least two of theporous matrixes are disposed in a sandwich like structure comprising atleast one layer of pre-transformed material. At times, the 3D object maybe formed from a porous matrix that does not comprise a layer ofpre-transformed material. The porous matrix may serve as an intermediatestep in the formation of a 3D object. For example, the porous matrix maybe (e.g., subsequently) densified during formation of the 3D object. Insome embodiments, the 3D object is formed by re-transforming (e.g.,melting) at least a portion (e.g., the entire) porous matrix into adenser material to form at least a portion of the 3D object. In someembodiments, the 3D object is formed from at least a portion of theporous matrix that is not densified.

At times, the porous matrix layer (e.g., set thereof) has a controlledporosity value. The PMX layer may comprise at most about 10%, 20%, 30%,40%, 50%, or 60% material, calculates as volume per volume, or area/areaporosity, e.g., of a cross-section plane of maximum porosity. The PMXlayer may comprise any suitable percentage between the afore-mentionedvalues (e.g., from about 10% to about 60%, from about 10% to about 40%,or from about 40% to about 60% material (v/v, or area/area porosity,e.g., of a cross-section plane of maximum porosity)). The porous matrixstructure may be formed by irradiation of the material bed portion bythe energy beam. For example, the beam cross-section of the energy beammay be (e.g., substantially) constant, or vary during the 3D printing.At times, the footprint of the energy beam on the exposed surface of thematerial bed may vary during formation of the porous matrix.

In some embodiments, the transforming energy beam irradiates a targetsurface. The energy beam (e.g., forming the PMX) may have any suitableenergy beam characteristics disclosed herein. For example, thecharacteristics may comprise wavelength, charge, power, power per unitarea, amplitude, trajectory, footprint, cross-section, focus, intensity,energy, path, or hatching characteristics described. herein. FIG. 3shows top-down view examples of various paths along which the energybeam may travel. The path may have any suitable shape (e.g., paths310-316), and can be continuous (e.g., 310, 311 or 316) or discontinuous(e.g., 312, 313, 314, or 315). The discontinuous path may compriseintervals at which the energy beam is (e.g., substantially) stationary.The (e.g., substantially) stationary energy beam may form a tile oftransformed material in the material bed. At least two sequential tilesmay overlap each other at least in part. The tiles may overlap. Theoverlapped area may be at least about 10%, 20%, 30%, 40%, 50%, 60%, 70%,80% or 90% of the average or mean tile area. The overlapped area may beat most about 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80% or 90% of theaverage or mean tile area. The overlapped area may between any of theafore-mentioned values (e.g., from about 10% to about 90%, from about10% to about 50%, or from about 40% to about 90%) of the average or meantile area. The percentage of overlapped area may be (e.g.,substantially) identical along the path of the energy beam forming thetiles. During the formation of the tile, the energy beam may be (e.g.,substantially) stationary. Tire transforming energy beam (e.g., formingthe PMX) may be any energy beam disclosed herein (e.g., having anyenergy density disclosed herein).

In some embodiments, the type-2 energy beam has an extended crosssection. For example, the type-2 energy beam has a FLS (e.g., crosssectional diameter) may be larger than the type-1 energy beam. The FLSof a cross section of the type-2 energy beam may be at least about 0.05millimeters (mm), 0.1 mm, 0.2 mm, 0.3 mm, 0.4 mm, 0.5 mm, 0.8 mm, 1 mm,1.5 mm, 2 mm, 2.5 mm, 3 mm, 3.5 mm, 4 mm, 4.5 mm, or 5 mm. The FLS of across section of the type-2 energy beam may be between any of theafore-mentioned values (e.g., from about 0.05 mm to about 5 mm, fromabout 0.05 mm to about 0.2 mm from about 0.3 mm to about 25 mm, or fromabout 2.5 mm to about 5 mm). The cross section of the energy beam can beat least about 0.1 millimeter squared (mm²), or 0.2. The FLS (e.g.,diameter) of a cross-section of the energy beam can be at least about 50micrometers (μm), 70 μm, 80 μm, 100 μm, 150 μm, 200 μm, 250 μm, 300 μm,350, 400 μm, 500 μm, or 600 μm. In some embodiments, the distancebetween the first position and the second position (e.g., distancebetween tile centers or tile boundaries) is at least about 50micrometers (μm), 70 μm, 80 μm, 100 μm, 200 μm, 250 μm, 300 μm, 350 μm,400 μm or 450 μm. In some embodiments, the distance between the firstposition and the second position (e.g., distance between tile centers)is at least about 50 millimeters (mm), 100 mm, 150 mm, 200 mm, 300 mm,400 mm or 500 mm. In some embodiments, the distance between the firstposition and the second position (e.g., distance between tile centers)is at least about 10 micrometers (μm), 15 μm, 20 μm, 25 μm, 30 μm, or 35μm. The spot size of the energy beam (e.g., at the target surface) canbe at least about 50 micrometers (μm), 55 μm, 60 μm., 65 μm, 70 μm, 75μm, 80 μm, 85 μm, 90 μm, 95 μm, 100 μm, 150 μm, 200 μm, 250 μm, 300 μm,350, 400 μm, 500 μm, 600 μm, 700 μm, 800 μm, 900 μm, 1000 μm or 11500μm. The FLS may be measured at full width half maximum intensity of theenergy beam. In some embodiments, the type-2 energy beam is a focusedenergy beam. In some embodiments, the type-2 energy beam is a defocusedenergy beam. The energy profile of the type-2 energy beam may be (e.g.,substantially) uniform (e.g., in the beam cross sectional area thatforms the tile). The energy profile of the type-2 energy beam may be(e.g., substantially) uniform during the exposure time (e.g., alsoreferred to herein as tiling time, or dwell time). The exposure time(e.g., at the target surface) of the type-2 energy beam may be at leastabout 0.1 milliseconds (msec), 0.2 msec, 0.3 msec, 0.4 msec, 0.5 msec, 1msec, 10 msec, 20 msec, 30 msec, 40 msec, 50 msec, 60 msec, 70 msec, 80msec, 90 msec, 100 msec, 200 msec, 400 msec, 500 msec, 1000 msec, 2500msec, or 5000 msec. The exposure time (e.g., at the target surface) ofthe type-2 energy beam may be at most about 10 msec, 20 msec, 30 msec,40 msec, 50 msec, 60 msec, 70 msec, 80 msec, 90 msec, 100 msec, 200msec, 400 msec, 500 msec, 1000 msec, 2500 msec, or 5000 msec. Theexposure time may be between any of the above-mentioned exposure times(e.g., from about 0.1 msec to about 5000 msec, from about 0.1 to about 1msec, from about 1 msec to about 50 msec, from about 50 msec to about100 msec, from about 100 msec to about 1000 msec, from about 20 msec toabout 200 msec, or from about 1000 msec to about 5000 msec). Theexposure time may be the dwell time. The power per unit area of thetype-2 energy beam may be at least about 100 Watts per millimeter square(W/mm²), 200 W/mm², 300 W/mm², 400 W/mm², 500 W/mm², 600 W/mm², 700W/mm², 800 W/mm², 900 W/mm², 1000 W/mm², 2000 W/mm², 3000 W/mm², 5000W/mm², or 7000 W/mm². The power per unit area of the type-2 energy beammay be at most about 100 W/mm², 200 W/mm², 300 W/mm², 400 W/mm², 500W/mm², 600 W/mm², 700 W/mm², 800 W/mm², 900 W/mm², 1000 W/mm², 2000W/mm², 3000 W/mm², 5000 W/mm², 7000 W/mm², 8000 W/mm², 9000 W/mm², or10000 W/mm². The power per unit area of the type-2 energy beam may beany value between the afore-mentioned values (e.g., from about 100 W/mm²to about 3000 W/mm², from about 100 W/mm² to about 5000 W/mm²from about100 W/mm² to about 9000 W/mm², from about 100 W/mm² to about 500 W/mm²,from about 500 W/mm² to about 3000 W/mm², from about 1000 W/mm² to about7000 W/mm², or from about 500 W/mm² to about 8000 W/mm²). The type-2energy beam may emit energy stream towards the target surface in a stepand repeat sequence.

In some embodiments, the type-2 energy beam comprises (i) an extendedexposure area, (ii) extended exposure time, (iii) low power density(e.g., power per unit area) or (iv) an intensity profile that can fillan area with a flat (e.g., top head) energy profile. Extended may be incomparison with the type-1 energy beam. The extended exposure time maybe at least about 1 millisecond and at most 100 milliseconds. In someembodiments, an energy profile of the tiling energy source may exclude aGaussian beam or round top beam. In some embodiments, an energy profileof the tiling energy source may include a Gaussian beam or round topbeam. In some embodiments, the 3D printer comprises a type-1 energybeams. In some, embodiments, an energy profile of the hatching energymay comprise a Gaussian energy beam. In some embodiments, an energyprofile of the type-1 energy beam may exclude a Gaussian energy beam.The type-1 energy beam may have any cross-sectional shape comprising anellipse (e.g., circle), or a polygon (e,g, as disclosed herein). Thetype-1 energy beam may have a cross section with a diameter of at leastabout 25 μm, 50 μm, 100 μm, 150 μm, 200 μm, or 250 μm. The type-1 energybeam may have a cross section with a diameter of at most about 40micrometers , 50 μm, 6 μm, 70 μm, 80 μm, 100 μm, 150 μm, 200 μm, or 250μm. The type-1 energy beam may have a cross section with a diameter ofany value between the afore-mentioned values (e.g., from about 40 μm toabout 240 μm, from about 40 μm, to about 100 μm, from about 50 μm toabout 150 μm, or from about 150 μm to about 250 μm). The power density(e.g., power per unit area) of the type-1 energy beam may at least about5000 W/mm², 10000 W/mm², 20000 W/mm², 30000 W/mm², 50000 W/mm², 60000W/mm², 70000 W/mm², 80000 W/mm², 90000 W/mm², or 100000 W/mm². The powerdensity of the type-1 energy beam may be at most about 5000 W/mm², 10000W/mm², 20000 W/mm², 30000 W/mm², 50000 W/mm², 60000 W/mm², 70000 W/mm²,80000 W/mm², 90000 W/mm², or 100000 W/mm². The power density of thetype-1 energy beam may be any value between the afore-mentioned values(e.g., from about 5000 W/mm² to about 100000 W/mm², from about 10000W/mm² to about 50000 W/mm², or from about 50000 W/mm² to about 100000W/mm²). The hatching speed of the type-1 energy beam may be at leastabout 50 millimeters per second (mm/sec), 100 mm/sec, 500 mm/sec, 1000mm/sec, 2000 mm/sec, 3000 mm/sec, 4000 mm/sec, or 50000 mm/sec. Thehatching speed of the type-1 energy beam may be at most about 50 mm/sec,100 mm/sec, 500 mm/sec, 1000 nm/sec, 2000 mm/sec, 3000 mm/sec, 4000mm/sec, or 50000 nm/sec. The hatching speed of the type-1 energy beammay any value between the afore-mentioned values (e.g., from about 50mm/sec to about 50000 mm/sec, from about 50 mm/sec to about 3000 mm/sec,or from about 2000 mm/sec to about 50000 nm/sec). The type-1 energy beammay be continuous or non-continuous (e.g., pulsing). In someembodiments, the type-1 energy beam compensates for heat loss at theedges of the target surface after the heat tiling process (e.g., formingthe tiles by utilizing the type-2 energy beam). The type-1 energy beammay be continuously moving along the path. The type-2 energy beam maystop and move along the path (e.g., the type-2 energy beam may transforma portion of the material bed along a path of tiles during the “stop”time and cease to transform the material bed along the path of tilesduring the “move” time.

In some embodiments, the first bottom skin layer is formed using (i) aconstant velocity and pulsing transforming energy beam (ii) a duty cycleenergy beam wherein the duty cycle comprises a dwell time and a delay meof irradiating the energy beam, the energy beam may be moved from afirst location to a second location during the delay time, (iii) a roundcross section, dithering energy beam that may be perpendicular to thedirection of growth of the layer of the forming 3D object, or (iv) anycombination thereof. At times, the bottom skin layer may be extended(e.g., as a wire, ledge, or a 3D plane) from a rigid-portion (e.g.,core) using a type-2 energy beam that may have a (i) circular footprint,or (ii) an elongated footprint. The type-2 energy beam may travel alonga trajectory. The trajectory may comprise a back and fourth motion (maybe referred to as a “retro scan”) along an overall forward direction.

In some embodiments, the first bottom skin layer is formed using aporous matrix structure. The porous matrix structure is formed using (i)a type-2 energy beam and/or (ii) a type-1 energy beam. The porous matrixstructure may comprise (i) a portion of transformed material portionand/or (ii) a portion of pores. The transformed material portion maycomprise a microstructure. The microstructure may be any microstructuredescribed herein. At times, the porous matrix structure may be tilled(e.g., occupied) with pre-transformed material. The porous matrix layermay be transformed (e.g., hardened, densified) by way of melting theporous matrix layer. The transforming energy beam may perform melting.Melting may be performed by forming one or more melt pools on a portionof the porous matrix structure. For example, FIGS. 15A-15D illustrateexample operations (e.g., for forming a bottom skin layer) using aporous matrix layer. FIG. 15A shows an example of a material bed (e.g.,1500) that comprises pre-transformed material (e.g., 1505). FIG. 15Bshows an example of irradiating (e.g., and transforming, e.g., sinteringand/or melting) a portion of the pre-transformed material within thematerial bed using a transforming energy beam (e.g., 1510). Thepre-transformed material may be transformed to a porous matrix layer(e.g., 1515). The amount of porosity within the porous matrix layer maybe controlled (e.g., using a controller, e.g., in real time duringformation of the PMX). Controlling may comprise adjusting at least onecharacteristic of the transforming energy beam (e.g., power per unitarea). FIG. 15C shows an example of irradiating a portion of the porousmatrix layer (e.g., 1520) within the material bed (e.g., 1522), using atransforming energy beam (e.g., 1521). The transforming energy beam maybe moved from a first location to a second location. The transformingenergy beam may form a melt pool at the first location and the secondlocation (e.g. 1523). The gray scale of the melt pools shows thepropagation of their formation, with a lighter melt pool being formedafter a darker melt pool. The transforming energy beam may move in adirection along, or at an angle with respect to the direction of growthof the porous layer, to form the at least one melt pool (e.g., 1523).For example, the transforming energy beam may move in a directionperpendicular to the direction of growth of the porous layer, to formthe at least one melt pool. The transforming energy beam that generatesthe melt pool(s) transforms the porous layer to a transformed materiallayer (e.g., that subsequently hardens). FIG. 15D shows an example of atransformed material layer (e.g., 1535), that is denser that the porousmatrix which served as its precursor.

In some embodiments, the first layer forming the bottom skin layer has aheight that is greater than the average height of one or more subsequentlayers. For example, the bottom skin layer may have a height of at leastabout 100 μm, 200 μm, 300 μm, 400 μm, or 500 μm. The one or moresubsequent layers to a porous matrix may be layers of particulatematerial (e.g., powder). The subsequent layers may comprise subsequentporous matrix layers (or layer portions) and/or (e.g., fully) denselayers of hardened material (or layer portions thereof). The one or moresubsequent layers may be of (e.g., substantial) similar FLS (e.g.,height). The one or more subsequent layers may comprise at least 1, 2,3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90, or 100 layers.The one or more subsequent layers may comprise at most 1, 2, 3, 4, 5, 6,7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90, or 100 layers. The one ormore subsequent layers may comprise any number of layers between theafore-mentioned values (e.g., from 1 to 100 layers, from 1 to 50 layers,or from 50 to 100 layers). The subsequent layers may be transformed(e.g., and subsequently further re-transformed) using the transformingenergy beam. At times, the energy beam may be a defocused energy beam.At times, the energy beam may be a focused energy beam. Transforming theone or more subsequent layers may form one or more layers of transformedmaterial respectively. At least two of the transformed one or morelayers may have at least one contact point (e.g., connection point) witheach other. At least one of the transformed one or more layers may haveat least one contact point with a porous matrix (or a transformed porousmatrix). At least one of the transformed, one or more layers may have atleast one contact point with a rigid-portion of the 3D object (e.g.,core). At least one of the transformed one or more layers may have atleast one contact point with a bottom skirt layer. The process offorming a porous matrix (e.g., set) and its transformation to form adenser portion of the 3D object may repeated during the 3D printing ofthe requested 3D object.

At times, a porous matrix (e.g., set) is transformed to form a firsttransformed material, and on top of the first transformed material, asecond porous matrix (e.g., set) is formed and subsequently transformedto form a second transformed material as part of the 3D object. Theporous matrix set may be transformed into a dense material using anenergy beam. At least a portion of the porous matrix may be filled witha pre-transformed material. An energy beam may irradiate the porousmatrix (e.g., set) to transform it into a denser structure. The denserstructure may be more compact than the porous matrix by about 1.5*, 2*,5*, 10*, 20*, 30*, 40*, 50 times (“*”). The denser structure maycomprise at least about 70%, 75%, 80%, 85%, 90%, 95%, 97%, 98%, 99%,99.5% material (percentages are calculated as volume per volume, orarea/area porosity, e.g., of a cross-section plane of maximum porosity).The denser structure may comprise a material percentage between theafore-mentioned percentage values (e.g., from about 70% to about 99.5%,from about 70% to about 90%, or from about 85% to about 99.5% material.Percentages are calculated as volume per volume, or area per areaporosity, e.g., of a cross-section plane of maximum porosity). At times,at least one surface (e.g., exposed bottom skin surface) of the densematerial 3D structure may be (e.g., substantially smooth). Substantiallyis relative to its intended purpose. The average or mean heightvariation in the surface may be at least about 10 μm, 15 μm, 20 μm, 25μm, 30 μm, 35 μm, 40 μm, 45 μm, 50 μm, 55 μm, 60 μm, 65 μm, 70 μm, 75μm, 80 μm, 85 μm, 90 μm, 95 μm, or 100 μm. The average or mean heightvariation in the surface may be at most about 10 μm, 15 μm, 20 μm, 25μm, 30 μm, 35 μm, 40 μm, 45 μm, 50 μm, 55 μm, 60 μm, 65 μm, 70 μm, 75μm, 80 μm, 85 μm, 90 μm, 95 μm, or 100μm. The average or mean heightvariation in the surface may be between any of the afore-mentionedvalues (e.g., from about 10 μm to about 100 μm, from about 10 μm toabout 30 μm, from about 30 μm to about 70 μm, or from about 70 μm toabout 100 μm).

Without wishing to be hound to theory, the hardened material within theporous matrix may provide one or more wetting surfaces for the liquidmaterial (e.g., whether transformed or pre-transformed material). Forexample, the hardened material within the porous matrix may provide oneor more wetting surfaces for a molten metal. For example, the hardenedmaterial within the porous matrix may provide one or more wettingsurfaces for a liquid polymer. The wetting surface may wet by the liquid(e.g., pre-transformed or transformed material). The wetting surface mayform paths and/or channels along which the liquid (e.g., transformedmaterial) travels. The wetting surfaces may provide directionalityduring the re-transforming (e.g., re-melting) operation and subsequenthardening (e.g., solidification) to form the denser (e.g., high density)material in at least a (e.g., pre-designed) portion of the 3D object. Atleast a portion of the porous matrix may form a skeleton for the forming3D object. For example, at least a portion of the porous matrix may forma skeleton for the dense portion of the 3D object.

In some embodiments, the porous matrix comprises a skeleton. Theskeleton may direct liquid (e.g., transformed) material in a particular(e.g., designed) manner. Forming a denser structure from the porousmatrix (e.g., more compact) may comprise re-melting at least a portionof the porous matrix. Forming a denser structure from the porous matrix(e.g., more compact) may comprise filling at least a portion of theporous matrix with pre-transformed material, and re-melting at least aportion of the porous matrix with at least a portion of the newlyintroduced pre-transformed material. The porous matrix may facilitateformation of a 3D object comprising functionally graded material. The 3Dobject comprising the functionally graded material may comprise at leasttwo portions having materials of different density and/ormicrostructures. The porous matrix may be utilized in the formation offunctionally graded material. The functionally graded material maycomprise at least two portions of the 3D object that have differentdensities (e.g., FIG. 20A, 2011, 2012, 2013, 2014, and 2015). Thedifferent densities may be pre-designed and/or controlled. The densitiesmay be formed by controlling at least one characteristic of the energybeam. For example, the densities may be formed by attenuating the powerdensity of the energy beam, its footprint on the target surface, or itstrajectory (e.g., to form a certain geometry). FIG. 20A shows an exampleof a functionally graded material comprising plurality of densities,cavities, hardened material structure and/or pore structure. The whiteareas in FIGS. 20A and 20B designate pores, and the black areasdesignate hardened material. The cavities may have a uniform shape(e.g., geometrical, homogenous, heterogeneous). The cavity may not beuniform in shape (e.g., random). The cavity may represent a portion ofthe 3D object (e.g., a geometrical subset such as FIG. 20A, 2012, 2013may represent a columnar cavity within the 3D object). The density of acavity may be pre-designed based on a requested property (e.g.,strength, tension, malleability, conductivity) of the portion of the 3Dobject represented by the cavity. The 3D object formed using the porousmatrix as an intermediate 3D object state, may be (e.g., substantially)less deformed compared to a 3D object that is formed by directlytransforming the pre-transformed material into the 3D object withoutusing the porous matrix as an intermediate state. Without wishing to bebound by theory, the porous matrix may facilitate wetting of the forming3D object surface and/or conducting heat through one or more layers ofthe forming 3D object.

In some embodiments, the one or more layers of pre-transformed material(e.g., including the PMX structure) are transformed (e.g., hardened)using at least one minimum threshold value. The minimum threshold valuemay be (i) of a temperature at a position (e.g., irradiation position)of the target surface, (ii) of the power density of the transformingenergy beam, or (iii) of the power of the energy source (e.g.,generating the type-1 energy beam). At tunes, transforming includesforming one or more melt pools. Heat may be diffused homogeneously orheterogeneously (e.g., in materials with non-uniform heat conductivity,at a shallow angle of the geometry of the 3D object, a wedge) across oneor more melt pools. At times, the one or more melt pools may be adjacentto each other. At times, the one or more melt pools may be distant fromeach other. At times, the melt pools may reach the bottom skin layer ofthe transformed material (e.g., when they were formed at least one layerabove the bottom skin layer). At times, the depth of the melt pool maybe controlled.

In some embodiments, the PMX structure is transformed (e.g., hardened,densified) by forming one or more melt pools that melt through the(e.g., entire) porous matrix structure (e.g., comprising a plurality ofPMX layers, e.g., FIG. 18A, 1802-1804). One or more melt pools may beformed (e.g., FIG. 18B, 1820) by irradiating an energy beam (e.g., atype-2 energy beam and/or a type-1 energy beam, e.g., 1825) through oneor more layers (e.g., highly porous PMX layers, denser PMX layers, mixeddensity layers, or a combination thereof) of the porous matrixstructure. During melt pool formation, the transforming energy beam maybe a stationary energy beam or a continuously moving energy beam. Thetransforming energy beam may have a narrow cross section (e.g., type-1energy beam (or a wide cross section (e.g., type-2 energy beam). One ormore characteristics (e.g., power per unit area, footprint, crosssection, velocity, FLS (i.e., diameter), dwell time or delay time) ofthe transforming energy beam may be controlled, when forming the one ormore melt pools. The period of time a melt pool remains molten may becontrolled (e.g., by controlling a characteristic of the transformingenergy beam). Control may be in real time (e.g., when forming a meltpool, when forming a second melt pool adjacent to the first melt pool).Control may be manual. Control may be pre-determined (e.g., feed-forwardcontrol). Control may be in real-time (i.e., using a feedback controlloop). The one or more layers of the PMX structure may be transformed(e.g., melted through) until the bottom layer of the porous matrixstructure plastically yields (e.g., softens). At times, the one or morelayers of the porous matrix structure may be transformed (e.g., meltedthrough) until at least one of (i) a portion of the bottom layer of theporous matrix attaches to a previously transformed layer (e.g., hardenedlayer) of the forming 3D object, (ii) a portion of the bottom skin layerof the portion of the 3D object or the porous matrix plastically yields,or (iii) a portion of the bottom skin may be transformed (e.g., molten).For example, FIGS. 14A-14B show examples of transforming a porous matrixstructure using the transforming energy beam. FIG. 14A shows an exampleof an irradiating type-1 energy beam (e.g., 1401) that forms a melt pool(e.g., 1402) within the porous matrix (e.g., 1403), that is formed ofthree different layers of porous material (e.g., which melt pool has ahigh aspect ratio). The layers of the PMX structure may optionally befilled with pre-transformed material (e.g., prior to transformation ofthe PMX structure). In the illustrated example of FIG. 14A, a narrowhigh power (e.g., hatching) energy beam forms an elongated, a smalldiameter, and deep melt pool that propagates (e.g., melts) through morethan one layer of the porous matrix (e.g., 1403), (e.g., until thebottom surface of the bottom skin layer of the porous matrix). Thediameter of the melt pool may be at least the size of the footprint ofthe irradiated type-1 energy beam. The porous matrix includes one ormore layers that may have different amounts of porosity. The porousmatrix may be formed on a platform (e.g. 1404). The porous matrix may beformed on top of the transformed layer, that resides on the targetsurface (e.g. 1414). FIG. 14B shows an example of a type-2 energy beam(e.g., 1411) that forms a melt pool (e.g., 1420) within the porousmatrix (e.g., 1413 and 1428) and the transformed material layer (e.g.,1425). In the illustrated example, the irradiating type-2 energy beamforms a wide, symmetric, conductive, and deep melt pool that spans(e.g., melts through) more than one layer of the porous matrix structure(e.g., till the bottom surface of the bottom layer of the porous matrix1428) and through the transformed layer (e.g., the bottom surface of thetransformed layer 1425).

In some embodiments, a hanging structure is formed as part of a 3Dobject. The hanging structure may be connected to at least one rigidportion that is a portion of the 3D object. The path of the transformingenergy beam may form an angle (e,g, perpendicular) relative to thedirection of growth of the one or more layers (e.g., anchorlesslysuspended layer, ledge, or cavity ceiling). For example, the path (e.g.,comprising hatches) of the transforming energy beam may form an angle(e.g., perpendicular) relative to the direction of growth of the hangingstructure. FIG. 21B shows a top view example of a direction of a hangingstructure wherein the moving energy beam forms a 90-degree anglerelative to the direction of growth of a layer that is at least aportion of the hanging structure. In the example of FIG. 21B, theforming layer 2101 of the 3D object is connected (e.g., anchored) to arigid-portion (e.g., 2130). The forming layer may be parallel to thetarget surface (e.g., exposed surface of the material bed) and/orplatform. The layer of the forming 3D object may be formed within thematerial bed. For example, the transforming energy beam may be moving(e.g., indicated by the vertical arrows in the FIG. 21B, 2112) at anangle perpendicular (e.g., 90°) to the direction of growth of the layer(e.g., 2105) at a first area on the target surface (e.g., comprisingarrow 2112). The moving energy beam may be moved from the first area onthe target surface to a second area on the target surface (e.g., from anarea comprising 2112 to an area comprising 2110). In the example of FIG.21B, the arrows on layer 2101 represent the path along which the energybeam travels, and arrow 2105 represents the general progression of theenergy beam path. The lighter arrows represent more recent paths, whilethe darker arrows represent older paths. The path may be any pathdescribed herein. The transforming energy beam may move at a constant orvaried velocity. At times, the transforming energy beam may be turnedoff for a period of time (e.g., delay time). Delay time may be at leastabout 1 (micro) μsec, 2 μsec, 5 μsec, 10 μsec, 20 μsec, 50 μsec, 100μsec, 200 μsec, 500 μsec, 1 (milli) msec, 2 msec, 5 msec, 10 msec, 20msec or about 50 msec. Delay time may be at most about 1 (micro) μsec, 2μsec, 5 μsec, 10 μsec, 20 μsec, 50 μsec, 100 μsec, 200 μsec, 500 μsec, 1(milli) msec, 2 msec, 5 msec, 10 msec, 20 msec or about 50 msec. Delaytime may be any ranges between the afore-mentioned times (e.g., fromabout 1 μsec to about 50 msec, from about 1 μsec to about 200 μsec, fromabout 200 μsec to about 10 msec, or from about 10 msec to about 50msec). The transforming energy beam may be moved from a first area to asecond area on the target surface. The transforming energy beam may beturned off when moving from the first location to the second location.FIG. 21A shows an example of turning off a transforming energy beam. Forexample, the transforming energy beam may be turned on at a firstlocation (e.g., 2121) for a period of time. This time may be describedas the “dwell time”. The transforming energy beam may be turned off fora period of time (e.g., FIG. 21A, d1, d2, d3, and d4). This period oftime may be described as the “delay time”. The dwell time in at leasttwo of the locations (e.g., 2121, 2122, 2123, 2124, and 2125) may be thesame. The dwell time in at least two of the locations may be different(e.g., 2121, 2122, 2123, 2124, and 2125). The delay time of at least twointermissions may be the same (e.g., d1, d2, d3, and d4). The delay timeof at least two intermissions may be different (e.g., d1,d2, d3, andd4). The transforming energy beam may be moved from a first location toa second location during the dwell time. The transforming energy beammay be moved from a first location to a second location during the delaytime. The transforming energy beam may be moving at a constant velocitywhen moving from the first location to the second location. The firstlocation may be adjacent to the second location. The first location maybe distant from the second location. The distance between two adjacentpaths of the transforming energy beam (e.g., hatching) may be prescribedbased on a requested porosity level of the porous matrix, 3D object,and/or requested structure of the 3D object (or respective portionsthereof).

In some embodiments, the transforming energy beam has an elliptical(e.g., circle) cross section. For example, the transforming energy beammay have a round cross section. The transforming energy beam may have anoval cross section. The transforming energy beam may be a dithering(e.g., wavering) energy beam. At times, a dithering energy beam (e.g.,retro scan) may be superimposed on the energy beam. The dithering energybeam may be at an angle (e.g., perpendicular) (i) to the direction ofmovement of the transforming energy beam, or (ii) to the direction ofgrowth of the portion of the 3D object. The angle may be at least about0°, 1°, 2°, 5°, 10°, 15°, 20°, 25°, 30°, 35°, 40°, 45°, 50°, 55°, 60°,65°, 70°, 75°, 80°, 85°, or 90°. The angle may be at most about 0°, 1°,2°, 5°, 10°, 15°, 20°, 25°, 30°, 35°, 40°, 45°, 50°, 55°, 60°, 65°, 70°,75°, 80°, 85°, or 90°. The angle may be any angle between theafore-mentioned values (e.g., from about 0° to about 90°, from about 0°to about 30°, from about 30° to about 60°, or from about 60° to about90°.

FIGS. 22A-22D shows examples of dithering energy beams (e.g., retroscan) forming melt pools. FIG. 22A illustrates an example of moving atransforming energy beam in six operations (e.g., 2210) in a forwarddirection (e.g., 2220) on a target surface (e.g., 2205) along a firstline. FIG. 22B illustrates an example of moving the transforming energybeam (e.g., 2235) four operations (e.g., 2230) in a backward direction(e.g., 2240) on the target surface (e.g., 2225) along a second line.FIG. 22C illustrates an example of moving the transforming energy beam(e.g., 2255) six operations (e.g., 2250) in the forward direction (e.g.,2260), on the target surface (e.g., 2245) along a third line. In theretro scan procedure, the operation illustrated in FIG. 22A is executed,followed by the operation illustrated in FIG. 22B, which is subsequentlyfollowed by the operation in FIG. 22C. The third line may partiallyoverlap the second line, which partially may overlap the first line. Thepartial overlapped lines may form an overall propagation of the firstline by the third line. Moving the transforming energy beam may includemoving one or more s selected from (i) moving in a forward direction toform a first forward path, (ii) irradiating to at least partiallyoverlap the first forward path in a backwards direction to form abackwards path, and (iii) irradiating to at least partially overlap thebackwards path in a forward direction. Operations (i) to (iii) can beconducted sequentially In some embodiments, the backwards path overlapsthe first forward path in part. In some embodiments, the second forwardpath overlaps the backwards path in part. Moving the energy beam mayinclude overall moving in the forward direction (e,g two steps forwardand one step backward). For example, when the non-overlapping secondforward path exceeds the first forward path in the direction of forwardmovement (e.g., in FIG. 22E, the difference between positions 7-8 on thetarget surface irradiated at time 15-16, and position 6 on the targetsurface irradiated at time 6). FIG. 22D illustrates an example of movingthe energy beam in three iteration positions, which circles (e.g., 2280)show an expansion of the superposition of a plurality of irradiatedpositions on the target surface 2265. In the first iteration, the energybeam moves six steps in the forward direction (e.g., irradiatingposition 2280). In the second iteration, the energy beam moves foursteps in the backward direction (e.g., irradiating position 2275) fromthe previous iteration. In the third step, the energy beam moves sixsteps in the forward direction (e.g., irradiating position 2270) fromthe earlier iteration, thus overall moving eight steps in the forwarddirection on the target surface (e.g., 2265). In the illustratedexample, the earliest irradiation position (e.g., first step) isindicated by the darkest gray circle. The shades of gray are lightenedto indicate the subsequent steps (from the earliest to the most recentirradiated position, e.g., step two to step six) in the iteration, andthe last irradiation position is indicated by a white circle. FIG. 22Eillustrates an example of a graphical representation of the retro scan,wherein the graphical representation illustrates the position of theirradiating energy on the target surface (e.g., 2285) as time (e.g.,2290) progresses. The retro scan may be performed with the transformingenergy beam (e.g., type-2 energy beam or type-1 energy beam) having anelliptical (e.g., circular) cross section. The retro scan may beperformed the transforming energy beam having an oval (e.g., Cartesianoval) cross section. The retro scan may be performed the transformingenergy beam having an elliptical cross section. The retro scan may beperformed continuously (e.g., during the 3D printing transformationoperation, or a portion thereof). The retro scan may be performed during(e.g., as part of) printing of the 3D object. The movement of the energybeam may be controlled statically (e.g., before or after printing of the3D object). The movement of the energy beam may be controlleddynamically (e.g., during printing of the 3D object). The elongatedenergy beam may be superimposed by an oscillating signal (e.g.,electronic signal). The oscillating signal may be generated by ascanner. The oscillating signal may further oscillate the retro scanmovement to generate an elongated energy beam.

In some embodiments, the retro scan is performed on an elliptical crosssection (e.g., elongated) energy beam. The retro scan can be performed,with any cross section of the irradiating energy (e.g., transformingenergy beam) disclosed herein. For example, the retro scan can beperformed using an elliptical cross section e.g., using the astigmatismmechanism). For example, the retro scan can be performed using acircular cross section (e.g., focused, defocused; having small or largeFLS). FIG. 23 shows an example of an astigmatism system for forming anelongated energy beam. The astigmatism system (e.g., FIG. 23, 2300) maybe coupled to the 3D printer. The astigmatism system may be disposedadjacent (e.g., in, or outside of) the processing chamber in which thetransforming energy beam generates the 3D object (e.g., FIG. 1, 126).The astigmatism system may be operatively coupled to an energy source,and/or to a controller. At least one element of the astigmatism systemmay be controlled before, after, and/or during at least a portion of the3D printing (e.g., in real time). At least one element of theastigmatism system may be controlled manually and/or automatically(e.g., using a controller). The energy source may irradiate energy(e.g., FIG. 23, 2305 depicting an energy beam). The astigmatism systemmay be used to form an elongated cross-sectional beam (e.g., narrow,and/or long. FIG. 23, 2340) that irradiates the target surface (e.g.,2335). The energy beam may be elongated along the X-Y plane (e.g., FIG.23). At times, the footprint of the energy beam may be elongated by anenergy beam perforation (e.g., an elongated slit) that the energy beammay be allowed to pass through. At nines, the movement of the energybeam may be controlled to perform a scan or a retro scan to form anelongated energy beam footprint.

In some embodiments, the astigmatism system includes two or more opticalelements (e.g., lenses. FIG. 23, 2310, 2330). The optical elements maydiverge or converge an irradiating energy (e.g., beam) that travelstherethrough. The optical elements may have a constant focus. Theoptical elements may have a variable focus. At times, the opticalelement may converge the rays of the energy beam. At times, the opticalelement may diverge the rays of the energy beam. For example, the firstoptical element may be a diverging lens. The astigmatism system maycomprise one or more medias (e.g., 2315. 2325). The medium may have ahigh refractive index (e,g., a high refractive index relative to thewavelength of the incoming energy beam). At least one medium may bestationary or translating (e.g., rotating along an axis, FIG. 23, 2320,2350). Translating may be performed before, after, or during at least aportion of the 3D printing. The first medium may translate along adifferent axis than the second medium. The translating axes of themediums may be different than (e.g., perpendicular to) the travelingaxis of the irradiating energy. For example, the first medium (e.g.,2315) may translate along the Z axis (e.g., 2320), the second medium(e.g., 2325) may translate along the Y axis (e.g., 2350), and theirradiating energy (e.g., 2305) may travel along the X axis. Thedistance between the media may be such that they do not collide witheach other when translating (e.g., rotating). The irradiating energy maybe directed to the second medium after it emerges from the first medium.The first optical element (e.g., 2310) may direct the energy beam to amedium (e.g., an optical window, e.g., 2315). The medium may (e.g.,substantially) allow the energy beam to pass through (e.g., may notabsorb a substantial portion of the passing energy beam). Substantiallymay be relative to the intended purpose of the energy beam (e.g., totransform the pre-transformed material).

In some embodiments, the optical astigmatism of the transforming energybeam refers to a resulting elliptical cross section of the transformingenergy beam that differs from a circle. Without wishing to be bound totheory, the different paths (e.g., lengths thereof) of the variousirradiating energy rays (e.g., 2351, 2352, or 2353), interacting withvarious thicknesses of the media (having an effective refractive index),may lead to an elongated cross section of the irradiating energy, andsubsequently to an elongated footprint of the irradiating energy on thetarget surface. The relative position of the first media (e.g., opticalwindow) and the second media may lead to an optical astigmatism. Thedegree and/or direction of the astigmatism may Vary (e.g., before,after, and/or during at least a portion of the 3D printing) in relationto the relative positioning of the two media. The degree and/ordirection of the astigmatism may be due to the relative positioning ofthe two media. The angular position of the media may be controlled(e.g., manually, and/or automatically). For example, the angularposition of the media may be controlled by one or more controllers.Controlling may include altering the angular position of the mediarelative to each other. Controlling may include altering the angularposition not relative to each other (e.g., relative to the targetsurface and/or to the energy source). Controlling the degree ofastigmatism may lead to controlling the length and/or width of theirradiating energy on the target surface. The irradiating energy may bedirected to a second optical element (e.g., FIG. 23, 2330) from the(e.g., first or second) medium. The second optical element may be aconverging lens. The converging lens may focus the irradiating energyafter its emergence from the (e.g., first or second) medium. Theconverging lens may translate (e.g., to vary the focus). The focusingpower of the lens (e.g., converging lens) may be variable (e.g.,electronically, magnetically, or thermally). The second optical elementmay be placed after the (e.g., first or second) medium. The energy beammay be directed (e.g., converged) on to a reflective element (e.g.,mirror, FIG. 23, 2345) and/or a seamier. The energy beam may be directed(e.g., converged) on to a beam directing element. The beam directing(e.g., reflective) element may be translatable. The beam directingelement may direct the energy beam to the target surface (e.g., materialbed, FIG. 23, 2335). The directed energy beam may be an elongated energybeam. The mirror may be highly reflective mirror (e.g., Berylliummirror).

In some embodiments, the diameter of the transforming energy beamfootprint is at least equal to the length of a forming bottom skin layer(e.g., ledge, wire, or plane). For example, the diameter of thetransforming energy beam footprint may be at least equal to the lengthof a forming hanging structure. At times, the diameter of thetransforming energy beam footprint may overlap with a previously formedportion of the 3D object to form a connection between the previouslyformed portion of the 3D object and the extending bottom skin layer(e.g., as part of a blade). For example, the diameter of thetransforming energy beam footprint may overlap with the rigid-portion(e.g., core), and thus form a connection between the rigid-portion andthe extending bottom skin layer (e.g., as part of a shelf) At times, thediameter of the transforming energy beam footprint may overlap with apreviously formed portion of the 3D object connected to the extendingbottom skin layer (e.g., as part of a hanging structure). At times, thelong axis of the elongated transforming energy beam footprint may be atleast equal to the length of the forming bottom skin layer (e.g., ledge,wire, or plane). At times, the long axis of the elongated transformingenergy beam footprint may overlap with a previously formed portion ofthe 3D object (e.g., the rigid-portion) that is connected to theextending bottom skin layer (e.g., as part of a ledge). At times, thecollective path (e.g., superimposed energy beam paths) of the ditheringenergy beam (e.g., retro scan) may be at least equal to the length ofthe forming bottom skin layer (e.g., ledge, wire, or plane). At times,the collective path (e.g., superimposed energy beam paths) of thedithering energy beam (e.g., retro scan) may overlap with therigid-portion (e.g., core) connected to the extending bottom skin layer.At times, the melt pools formed by the transforming energy beam mayoverlap with at least one previous layer of the forming 3D object. Insome cases, when transforming (e.g., melting) the (e.g., entire) porousmatrix set (e.g., termed herein as “re-transforming operation”), atleast one gas may be trapped within the transformed material, creatingtrapped pores in the otherwise dense material. At least onecharacteristic of the energy beam may be modified (e.g., as a functionof time) to allow these pores to escape. The characteristics of theenergy beam may comprise trajectory, delay-time, fluence, power per unitarea (i.e., power density), cross-section, focus/defocus, speed, energyprofile, or dwell time. The energy beam may have a constant energyprofile over time. At times, the energy beam may vary over time. Thevariation may be a tailing variation. The variation may be prescribed oradjusted in real-time (e.g., during the transforming operation). Attimes, the energy beam radiation may allow at least a portion of thetransformed (e.g., molten) porous matrix (e.g., set) to remain in thetransformed (e.g., molten) state for a period of time that allows theone or more gasses to escape, thus preventing their trapping uponsolidification.

FIG. 27 shows an example of energy source power as a function of time,or a power density of the energy beam as a function of time, wherein aphenomenon profile may pertain to the power of the energy source or thepower density of the energy beam, respectively. For example, FIG. 27shows an example of an initial increase in power density on turning theenergy beam) at followed by a plateau 2712 during a period from t₁ to t₂(e.g., when irradiating at a constant power density), followed by adecrease during a period 2713 from t₂ to t₃ (e.g., while decreasing thepower density as the transformed/transforming material heats beyond athreshold temperature), followed by a second plateau 2714 during aperiod from t₃ to t₄ (e.g., during an intermission when the energy beamis turned off). In some examples, the time span from t₁ to t₂ issubstantially zero e.g., and the plateau becomes a point). In someembodiments, the power density variation shown in FIG. 27 represents thepower density variation during a single energy pulse (e.g., laser energypulse) to form a corresponding melt pool. The transforming energy beammay travel along the target (e.g., exposed) surface while having a(e.g., substantially) constant or variable power density (i.e., powerper unit area). The variation may comprise initial increase in powerdensity, followed by a decrease in the power density, or any combinationthereof. The variation may comprise initial increase in power density,followed by a plateau, followed by a subsequent decrease in the powerdensity, or any combination thereof. The increase may be linear,logarithmic, exponential, polynomial, or any combination or permutationthereof. The decrease and/or increase may be linear, logarithmic,exponential, polynomial, or any combination or permutation thereof. Theplateau may comprise of a substantially constant energy density.

In some embodiments, the power density of the energy source is modifiedduring a transformation operation (e.g., during asingle-transformation-operation (STO)). In some transformation processes(e.g., STO), each pulse of the energy beam (e.g., laser beam) can beused to form a corresponding melt pool (thus forming a correspondingtile). During formation of the melt pool, the power density of theenergy beam can be controlled (e.g., in real time). The control can beusing a controller. The controller may use one or more sensormeasurements (e.g., of the irradiated portion and/or of the immediatevicinity of the irradiated portion). During formation of the melt pool,the power density of the energy beam can be (e.g., substantially)constant or Varied. An example of a power density variation during anenergy pulse is indicated in FIG. 27.

At times, the transformed material is overheated during melt poolformation. The overheating may cause departure of at least a portion ofthe transforming material, e.g., by evaporation, spitting, or plasmaformation.

In some embodiments, the power density is spiked to a maximum (P_(max))value, e.g., for a brief period of time. The brief period can be a smallt₁ to t₂ value, e.g., zero. Following the spike in the power density toP_(max), the power density of the energy beam can be reduced (e.g.,according to a function), until reaching a minimum power density levelP_(min) (e.g., zero). The function can comprise a linear, exponential ortrigonometric function (e.g., logarithmic function). The reduction maybe effectuated using energy beam modulation. Usage of an energy densityprofile comprising a short spike to P_(max) followed by a (e.g., steep)reduction to P_(min) during a pulse forming the melt pool, may preventoverheating of the melt pool (e.g., may prevent departure oftransforming material from the melt pool). That is, the maximum powerdensity of the energy beam can be sufficiently high to inducetransformation of the pre-transformed material (e.g., liquify a powderof pre-transformed material). For example, the maximum power (P_(max))at 2712 can be high and have a very short period (t₁ to t₂). In someembodiments, the period t₁ to t₂ is near zero. In some cases, the powerdensity diminishes from maximum power (P_(max)) gradually. In someembodiments, the power density is diminished in a controlled manner,e.g., in accordance with a function (e.g., as disclosed herein). In someembodiments, the maximum power density (P_(max)) and/or manner in whichthe power density is diminished can he controlled in real time (e.g.,dining formation of the melt pool, a path of tiles, or a layer of the 3Dobject). The magnitude of the power density spiking can be characterizedusing a ratio of the maximum power density (P_(max)) to the averagepower density (P_(average)), expressed as P_(max)/P_(average). TheP_(max)/P_(average) can vary depending on a number of factors. Thefactors may include, for example, the type of material of thepre-transformed material, the surface area, size and shape of theparticles of a powdered pre-transformed material (e.g., and their sizeand/or shape distribution), ambient temperatures and atmospheres (e.g.,pressure thereof), power of the energy source generating the energybeam, cross section of the energy beam, or any combination thereof. Insome embodiments, the P_(max)/P_(average) is at least about 1.5, 2.0,2.5, 3.0, 3.5, 4.0, 4.5, 5.0, 5.5, 6.0, 6.5, 7.0, 7.5, 8.0, 8.5, 9.0,9.5, 10.0, 10.5, 11.0, 11.5, 12.0, 12.5, 13.0, 13.5, 14.0, 14.5, 15.0,15.5, 16.0, 16.5, 17.0, 17.5, 18.0, 18.5, 19.0, 19.5, or 20.0. In someembodiments, the P_(max)/P_(average) ranges between any value betweenthe afore-mentioned values (e.g., about 1.5 and 20.0, between about 1.5and 12.0, between about 1.5 and 4.0, or between about 12.0 and 20.0).

In some embodiments, at least one characteristic of the energy beamforming the contour can be controlled, e.g., in real time during itsformation. For example, the power density and/or cross section of theenergy beam may be controlled, e.g., using a controller. The controllermay use one or more sensor measurements (e.g., of the irradiated portionand/or of the immediate vicinity of the irradiated portion). In someembodiments, a (e.g., real time) modified power density beam is used toform a contour (also referred to as a rim or perimeter portion) of apart.

In some embodiments, the energy beam radiation is used to form a rim ina hatch methodology (e.g., while continuously moving the energy beam).In some embodiments, the energy beam radiation is used to form a rim ina tiling methodology (e.g., while discontinuously moving the energybeam, e.g., in a step and repeat mode). At least one characteristic ofthe energy beam call be modified (e.g., in real time) duringirradiation. The modification of the energy beam may be controlled(e.g., manually and/or by a controller). The controller may compriseclosed loop, open loop, feedback, or feed-forward control. Thecontroller can be any controller and/or any control scheme disclosed inU.S. patent application Ser. No. 15/435,128, PCT patent applicationnumber PCT/US17/18191, or European patent application numberEP17156707.6, each of which is incorporated herein by reference in itsentirety where non-contradictory. The at least one characteristic maycomprise dwell time, intermission time, pulsing rate, average powerdensity (e.g., during dwell time and/or intermission), cross sectionalshape and/or FLS of the beam, beam power density profile over the beamcross section, or power density profile over time (e.g., during dwelltime and/or intermission). Tile modification of at least onecharacteristic of the energy beam may prevent overheating of thetransforming material along contours of a 3D object. The overheating maycause expulsion of the transformed material from the powder bed. (e.g.,as soot, droplets, plasma, or other form of debris). For example, themodification of at least one characteristic of the energy beam mayprevent departure of the transforming material from the rim. In someembodiments, at least one characteristic (e.g., the power density) ofthe energy beam is modified in accordance with a location along acontour of the part. In some embodiments, at least one characteristic(e.g., the power density) of the energy beam is modified in accordancewith various geometric characteristics (e.g., types of geometricvariations) along a contour of the part. The geometric characteristicsmay comprise degree of departure from a straight line or lack thereof(e.g., maintaining a straight path). For example, the geometriccharacteristics may comprise a curvature having a radius, or a variationdegree of a curvature (e.g., a steeply winding path, a gradually windingpath, an oscillating path such as a zigzag or sinusoidal path).Different types of controlled energy pulses (e.g., having differentpower density profiles) can be used to form the contour of a layer oftransformed material. The at least one characteristic of the energy beam(e.g., during a dwell time) may be adjusted in real time orpredetermined. The at least one characteristic of the energy beam may heroughly predetermined and fine-tuned in real time (e.g., during a dwelltime of the energy beam along the path such as along the rim).

Referring to FIG. 28A, for example, the type-1 energy beam used to formthe contour (rim) at position 2813 can have a first power densityprofile that is different from a second power density profile used toform the contour (rim) at position 2814, which can be different from athird power density profile used to form the interior portion atposition 2815. Similarly, referring to FIG. 36A, for example, the type-2energy beam used to form the contour (rim) at position 3613 can have afirst power density profile that is different from a second powerdensity profile used to form the contour (rim) at position 3614, winchcan be different from a third power density profile used to form theinterior portion 3615. In this way, the varied power density along acontour (rim) of a part can result in compensation for differentgeometric constraints of the resulting layer of transformed material.The variation in power density may consider material properties and/orgeometry of the (i) previously formed layers as part of the 3D object,(ii) subsequent (unformed) layers of the 3D object, (iii) the entire 3Dobject, or (iv) any combination thereof. The material properties maycomprise heat conductivity, porosity formation, stress buildup,elasticity of the material, or response to stress buildup. The responseto stress buildup may comprise internal tears and/or dislocations. Insome embodiments, a controller is configured to (e.g., automatically)adjust the power density profile of the energy beam along a contour. Theadjustment may comprise usage of a motion control (e.g., comprising feedforward control, feedback control, closed loop control, or open loopcontrol). In some cases, a control scheme (e.g., feed forward, feedback,closed loop, and/or open loop) is used to control one or morecharacteristics of a skin, e.g., by controlling the energy beam and/orenergy source. At times, a motion of the energy beam is controlled usingthe controller. For example, the controller controls a size and/or shapeof tiles. The control can be done in real time (e.g., during a 3Dprinting process)). For example, the control can he at least partiallybased on a signal from a melt pool during the printing process (e.g.,thermal reflectivity, and/or specularity). In some cases, the signal(e.g., temperature) of the target surface at the irradiated positionvaries (e.g., increases) during the minting process. The thermalincrease may be referred to as thermal build up. Real time control canbe used to compensate for thermal build up. In some embodiments, realtime control is used to form features (e.g., tiles) having (e.g.,substantially) the same size and/or shape. In some embodiments, realtime control is used to form features (e.g., tiles) having different(e.g., pre-determined) sizes and/or shapes. In some embodiments, thecontrol is performed without stopping the energy beam scanning and/orwithout stopping the 3D printing. In some embodiments, real time controlcomprises (i) directing an energy beam at a target (e.g.,pre-transformed material (e.g., powder) and/or hardened material (e.g.,previously transformed using a first transformation process), (ii)monitoring at least one characteristic (e.g., temperature) of the targetand/or the energy beam during (i), or (iii) adjusting at least onecharacteristic of the energy beam (e.g., power density,). For example,real time control can comprise (i), (ii) and (iii). In some embodiments,the monitoring in (ii) includes monitoring the thermal output of aregion of the target impinged by the energy beam (e.g., using photodiodetemperature sensor(s)) and/or a vicinity thereof (e.g., up to 6 FLSsfrom the center of the impinged target). The vicinity can be anyvicinity of the energy beam disclosed in U.S. patent application Ser.No. 15/435,128, PCT patent application number PCT/US17/18191, orEuropean patent application number EP17156707.6, each of which isincorporated herein by reference in its entirety wherenon-contradictory. The adjusting in (iii) can be performed while theenergy beam is directed at the target. This type of real time controlcan be used, for example during transformation to form a contour (e.g.,a rim). For example, the power density of an energy beam can be variedbased on real time control (e.g., comprising feedback control) in orderto form a smoother surface of the contoured area (having reducedroughness) and/or formed surface (e.g., sides of the 3D object that areformed by accumulation of rims one on top of another).

In some embodiments, irregular melt pools form within a complexstructure of a 3D object (e.g., comprising an overhang structure thatforms an angle of about 45, 35, or 30 degrees or lower, from a normal tothe gravitational field and/or a building platform), which complexstructure is at least a portion of the forming 3D object. The overhangstructure may form an acute (e.g., shallow, intermediate, or steep), orobtuse angle with respect to a normal to the gravitational field and/ora building platform. Without wishing to be bound by theory, theirregular melt pool may cause one or more defect (e.g., deformation) inthe forming 3D object. To avert the defect (e.g., warping) of theoverhang structure, a porous matrix (e.g., structure) can be used, whichporous matrix is subsequently densified to form a (e.g., substantially)defect free complex structure. In order to avert the formation of adefect (e.g., stresses and/or pores), a previously densified structurecan be re-transformed using an energy beam that re-transforms at least aportion of the densified structure. Elimination of defects may berealized by subjecting the complex structure to at least 1, 2, 3, 4, 5,6, 7, or 8 cycles or re-transforming. In some embodiments,re-transforming of at least a portion of the 3D object may form at leasta portion of the 3D object that has a lower degree of variation fromaverage surface plane (e.g., forming a smoother surface portion), ascompared to the at least a portion of the 3D object that has notundergone re-transformation. For example, the at least a portion of thesurface may assume a shiny metallic reflection. For example, the atleast a portion of the surface may have a high Ra value. FIGS. 16A-16Fillustrate example s for forming an overhang structure (e.g., a ledge)using the MTO process. FIG. 16A shows an example of a material bed(e.g., 1600) that comprises pre-transformed material disposed above aplatform (e.g., 1605), and an energy beam (e.g., 1615) irradiating(e.g., and transforming, e.g., sintering and/or melting) a portion ofthe pre-transformed material within the material bed using atransforming energy beam (e.g., 1615). In the example in FIG. 16A, thepre-transformed material is transformed to form a first porous matrixlayer (e.g., 1612), that partially overlaps a rigid-portion (e.g.,1614). The porous matrix may connect to the rigid-portion. The amount ofporosity within the first porous matrix layer (e.g., 1612) may becontrolled. Controlling may comprise adjusting at least onecharacteristic of the transforming energy beam (e.g., power per unitarea). The control may be real-time control during the transformation.FIG. 16B shows an example of irradiating a portion of the porous matrixlayer (e.g., 1625) within the material bed (e.g., 1620) using atransforming energy beam (e.g., 1621). The transforming energy beam maybe moved from a first location to a second location. The transformingenergy beam may form a melt pool at the first location and/or at thesecond location (e.g. 1627). The transforming energy beam may more alonga path. To form a layer of transformed porous matrix, the transformingenergy beam may form hatches in a direction along, or at an angle withrespect to the direction of growth of the porous layer (e.g., 1622), forexample, to form the at least one melt pool. To form a layer oftransformed porous matrix, the transforming energy beam may form hatchesin a direction perpendicular to the direction of growth of the porouslayer. To form a layer of transformed porous matrix, the transformingenergy beam may form hatches that form an angle between 0 degrees and 90degrees with respect to the direction of growth of the porous layer. Insome embodiments, one energy beam (e.g., type-2 energy beam)participates in the MTO process to both form the PMX layer (e.g., 1612)and densify it to form the denser layer (e.g., 1630). The energy beammay vary in at least one characteristic between operating in a mode offorming the PMX layer and operating in a mode of densifying the PMXlayer to form a denser layer. In some embodiments, two different energybeams participate in the MTO process. For example, a first beam (e.g.,1615) may form the PMX layer, and the second beam (e.g., 1621) maytransform and densify the PMX layer to form a denser layer. For example,a first beam (e.g., 1612) may form the PMX layer, and the second beam(e.g., 1621) may transform and densify the PMX layer to form a denserlayer. The first beam may be a type-1 energy beam. The second beam maybe the type-2 energy beam. The type-2 energy beam may be a power densitythat is lower than that of the type-1 energy beam (e.g., lower by atleast 3 times (*), 4*, 5*, 6*, 7*, 8*, 9*, 10*, 15*, or 20*). The type-2energy beam may be focused or defocused. The type-2 energy beam may havea larger cross section as compared to the type-1 energy beam (e.g.,larger by at least 2 times (*), 3*, 4*, 5*, 6*, 7*, 8*, 9*, 10*, 15*, or20*). During the MTO process, the type-2 energy beam may have dwell time(e.g., to form a tile) of about 40 milliseconds (msec), 50 msec, 60msec, 70 msec, 80 msec, 90 msec, 100 msec, or 500 msec. During the MTOprocess, the type-2 energy beam may have dwell time between any of theafore-mentioned dwell times (e.g., from about 50 msec to about 500 msec,from about 50 msec to about 100 msec, from about 60 msec to about 80msec, or from about 100 msec to about 500 msec). The transforming energybeam may generate the melt pools (e.g., 1627), and/or transforms thefirst porous layer to a transformed (e.g., the first porous layerhardens) material layer that is denser than the porous matrix layer. Theformed ledge may be connected to a rigid-portion or to a first formedlayer (e.g., ASBS). The rigid-portion may be anchored to the platform.The rigid-portion may be suspended anchorlessly in the material bed(e.g., 1614). Transforming may include (e.g., subsequent) solidificationof the one or more melt pools. FIG. 16C shows an example of atransformed material layer (e.g., 1630), that is denser than the firstporous layer that served as its precursor (e.g., 1612). FIG. 16D showsan example of dispensing a planar layer of pre-transformed material overthe first transformed material layer (e.g., FIG. 16C, 1630), andirradiating (e.g., and transforming, e.g., sintering and/or melting) aportion of the pre-transformed material layer within the material bed(e.g., 1640) using a transforming energy beam (e.g., 1645). Thepre-transformed material may be transformed to form a second porousmatrix layer (e.g., 1642) adjacent to (e.g., above) previouslytransformed layer (e.g., 1644) that is denser than the PMX layer. Theamount of porosity within the second porous matrix layer may becontrolled (e.g., in real time). FIG. 16E shows an example ofirradiating (e.g., and transforming) a portion of the second porousmatrix layer (e.g., 1655) within the material bed (e.g., 1650) using thetransforming energy beam (e.g., 1651). The transforming energy beam mayform one or more melt pools (e.g., 1652). The transforming energy beammay transform the second porous matrix layer e.g., 1652), by meltingthrough the second porous layer. In some embodiments, the transformedenergy beam transforms a portion of the PMX layer, as well as a portionof previously formed one or more layers (e.g., the first layer, e.g.,1653). Transforming at least a portion of a previously formed (e.g.,dense) layer along with transforming the PMX layer, may facilitateadhering of the transforming PMX layer to the previously formed (e.g.,dense) layer. For example, transforming at least a portion of the firstlayer (e.g., 1653) along with the transformation of the second PMX layer(e.g., 1655) may facilitate adhering of the transforming PMX layer(e.g., that results in the layer 1660) to the first densified layer(e.g., 1665). At times, transforming the PMX layer may includetransforming of a plurality of previously formed layer. At times, thetransforming energy beam may transform (e.g., re-transform) one or morepreviously transformed layers. FIG. 16F shows an example of multiple(e.g., two) transformed and densified material layers (e.g., 1650,1665), that are denser than the first PMX layer (e.g., 1612) and secondPMX layer (e.g., 1655) that served as their precursors. The twodensified layers (e.g., 1660 and 1665) in the example of FIG. 16F, areconnected to a rigid-portion (e.g., 1667), which together form at leasta portion of the 3D object, which is disposed in a material bed (e.g.,1669).

In some embodiments, a bottom skin is formed using the PMX (e.g., as anintermediate). The PMX bottom skin layer may be re-transformed to createa denser structure (e.g., denser bottom skin layer). The externalsurface of the resulting densified structure may be (e.g.,substantially) smooth. For example, the densified structure may be(e.g., substantially) free of hanging structure (e.g., stalactite-likestrictures). In one embodiment, a portion of the PMX bottom skin isre-transformed to generate a partial densified layer (e.g., densifiedmaterial) and a partial porous matrix layer. The one or morerigid-portions may be coupled to the PMX structure. Prior todensification of the PMX, the porous matrix may be filled at least inpart with pre-transformed (e.g., particulate) material. Once filled atleast in part, at least a portion of the PMX may be transformed usingthe transforming energy beam. When a plurality of layers (e.g., PMX orpre-transformed material layers) are transformed (e.g., using thetransforming energy beam), the process is also referred to herein as“deep tiling”). The term “deep tiling” refers herein to irradiating aplurality of layers (e.g., PMX, dense layers, and/or pre-transformedmaterial layers). The deep tiling process may result in forming a meltpool that spans more than one layer (e.g. >50 microns), that is, has aheight (e.g., FIG. 25A, 2510) of more than one layer. The layer size maybe defined by the 3D printing process (e.g., by a layer that isdispensed by the layer dispensing mechanism). For example, the height(e.g. FIG. 25A, 2510) of a melt pool in deep tiling can be in the rangeof about 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200,1300, 1400, 1500, 1600, 1700, 1800, 1900 or 2000 microns. The formationof the deep tiles can be initiated from a position adjacent to, orcomprising a previously formed 3D object portion (e.g., a rigidstructure). The formation of the deep tiles can he initiated from aposition adjacent to, or comprising the overhang. In some embodiments,the farthest tile from the previously formed 3D object portion (e.g.,rigid-portion) may be transformed last. In some embodiments, dieoperation is repeated until at least the overhang portion is completelydensified and reaches a minimum height threshold, after whichdeformation is not substantial. The threshold height may be, forexample, at least 1 mm, 1.5 mm, 2 mm, 2.5 mm, 3 mm, 3.5 mm, 4 mm, 4.5 mmand/or 5 mm, depending on the material of the material bed. The deeptile formed by deep tiling may protrude to at least about half the totalthickness of the forming 3D object. The deep tile formed by deep tilingmay protrude at least about two layers.

In some embodiments, the layer of transformed material (e.g., PMX ordensified PMX layer) comprises a portion that is susceptible todeformation (e.g., a weak portion). In some instances, such operationscheme may result in a layer (e.g., an overhang) in which the vulnerablelayer portion is the last transformed portion (e.g., tiled portion) thatcompletes the layer (e.g., overhang) of transformed material. Thevulnerable portion may be a portion that is susceptible to deformation.In some embodiments, to compensate for the deformation susceptibility ofa first vulnerable layer portion (which is situated in a first layer),one or more subsequent layers (e.g., a second layer) may be formed,which (e.g., micro and/or macro) structure is generated in a way thatalters the deformation (e.g., and/or susceptibility to deformation) ofthe resulting 3D object portion. The second layer may be a PMX layer.The first layer may be a PMX layer. The PMX layer (e.g., second and/orfirst. PMX layer) may have an inhomogeneous distribution ofmicrostructures and/or pores along the layer. The microstructureinhomogeneity may alter (e.g., reduce) the deformability of the layerportion that was considered to be a vulnerable portion if themicrostructure and/or porosity distribution would be homogenous. Whentwo successive layers have vulnerable portions, the position of thelayers may be designed such that the first vulnerable portion in thefirst layer and the second vulnerable portion in the second layer willnot re-enforce at least one of their respective vulnerability. Thevulnerable portions may be (e.g., vertically, and/or horizontally)misaligned. The vulnerable portions may be (e.g., vertically, and/orhorizontally) non-overlapping. For example, the first vulnerable portionshould not (e.g., vertically) align with the second vulnerable portion.The misalignment may be effectuated by altering the macro and/or microstructure of the layers (e.g., altering the microstructure of the PMXlayer) prior to their transformation to form a portion of the 3D object.The alteration of the structure may comprise a controllably alterationof the level of porosity (e.g., horizontally, and/or vertically) alongthe PMX layer. FIG. 33 shows an example of two PMX layers shown as avertical cross section. The first PMX layer comprises a vulnerableportion 3304, and a more robust portion 3303. The second PMS layercomprises a vulnerable portion 3301, and a more robust portion 3302. Thefirst PMX layer is anchored to a rigid-portion 3305. In the exampleshown in FIG. 33, the vulnerable portions (e.g., 3301 and 3304) are not(e.g., vertically) aligned to overlap with each other. In the exampleshown in FIG. 33, the vulnerable portions are (e.g., vertically)misaligned, and do not (e.g., vertically) overlap each other.

In some embodiments, deep tiling is performed when transforming one ormore layers (e.g., of pre-transformed material, PMX layer, and/ordensified material layer) to form the 3D object. Deep tiling may includeirradiating a target surface to transform through more than one layers(e.g., porous matrix set, pre-transformed material layers, ortransformed material layers). Deep tiling may include wetting (e.g.,melting) at least one previously deposited and/or formed layer. Deeptiling may be performed with a focused (e.g., hatching) or defocused(e.g., tiling) energy beam. Deep tiling may be performed with thescanning and/or type-2 energy beam. The energy beam may have a small orlarge cross section. The choice of cross section may relate to the widthof the overhang structure that is being formed. In some examples, whenforming a shallow angled overhang structure; (e.g., that may form abottom skin of a ledge and/or a cavity ceiling), wherein the overhang isnarrow, the process may require an energy beam having a narrower crosssection. FIG. 24 shows an example of extending a ledge of a forming 3Dobject having an exposed surface 2410. The ledge extension may compriseforming a PMX layer portion (e.g., 2400). The PMX layer may beirradiated using a transforming energy beam (e.g., 2420). In someexamples, a portion of one or more previous layers (e.g., having anexposed bottom surface 2405) may be transformed or at least contacted bythe transformed material. At times, a bottom surface of the forming 3Dobject (e.g., ledge having an exposed bottom surface 2405) may be wettedby the transformed (e.g., liquid) material. Wetting of the bottomsurface may alter the roughness of the bottom (skin) surface. Wetting ofthe bottom surface may result in a flatter bottom (skin) surface (e.g.,a smoother bottom surface). Wetting of the bottom surface may result inreducing the roughness of the bottom (skin) surface.

At times, deep tiling is performed to density one or more layers. Theone or more layers may comprise layers above the bottom skin layerand/or the rigid-portion (e.g., to form a thickened overhang structure).The one or more layers may include the bottom skin layer. Deep tilingmay include irradiating the energy beam to transform (e.g., melt)through more than one layers (e.g., pre-transformed material layer, PMXlayer, and/or dense material layers) Deep tiling may includetransforming (e.g., melting) at least one previous layer of the forming3D object. Deep tiling may include irradiating the energy beam totransform more than one previously formed (e.g., hardened, densified)layers of hard material (e.g., PMX or denser layers). FIGS. 18A-18Cshows examples of operations in transforming (e.g., re-melting) an(e.g., entire) porous matrix structure comprising a plurality ofindividually fabricated PMX layers, by melting through more than one PMXlayer of the PMX structure. FIG. 18A shows an example of a porous matrixcomprising multiple (e.g., three, 1802, 1803, 1804) PMX layers, within amaterial bed (e.g., 1801). FIG. 40A shows an example of a porous matrixsandwich structure comprising multiple (e.g., two (e.g., 4002 and 4004))PMX layers separated by a layer of pre-transformed material (e.g., 4003)in a material bed (e.g., 4001). At times, at least two of the PMX layersmay have (e.g., substantially) the same porosity. At times, at least twoof the PMX layers may have different porosity. FIGS. 18B and 40B showexamples of irradiating (e.g., and transforming, e.g., melting) throughthe multiple PMX layers, using a transforming energy beam (e.g., FIG.18B, 1825 or FIG. 40B, 4025) (e.g., a type-2 energy beam havingsufficient power density and/or operating under sufficient dwell time topenetrate the plurality of PMX layers). The irradiating may includeforming one or more melt pools (e.g., FIG. 18B, 1820 or FIG. 40B, 4020).Deep tiling may comprise low aspect ratio (e.g., shallow), homogeneouslydimensioned (e.g., hemispherical), or high aspect ratio (e.g., deep)melt pools. For example, the melt pool may have a high aspect ratio(e.g., as disclosed herein). For example, the melt pool may be deep. Forexample, the melt pool may be wide (e.g., have a low aspect ratio (e.g.,as disclosed herein). The deep tiling may penetrate a 3D object part.The penetration may be to a depth that facilitates plastic yielding of aparallel position to the footprint of the irradiating energy beam, whichparallel position is at least a portion of a bottom skin of the 3Dobject part. At times, the transformation may extend to (e.g., meltthrough) at most two layers, melt through at most three layers, or, meltthrough until the bottom skin layer (or a portion thereof) plasticallyyields. Deep may comprise melting through a plurality of layers of thefilming 3D object. FIGS. 18C and 40C show examples of transformed (e.g.,hardened, densified) portions of the 3D objects, that may be denser thanthe one or more PMX layers that were its precursor. In some embodiments,one energy beam (e.g., type-2 energy beam) participates in the PMX layer(set) formation (e.g., FIG. 18A or FIG. 40A) and in its densificationprocess (e.g., FIG. 18B or FIG. 40B) to form the denser layer (e.g.,FIG. 18C, 1830 or FIG. 40C, 4030). The energy beam may vary in at leastone characteristic between operating in a mode of forming the PMX layerand operating in a mode of densifying the PMX layer to form a denserlayer. In some embodiments, two different energy beams participate inthe MTO process. For example, a first beam (e.g., 1615) may form the PMXlayer, and the second beam (e.g., 1621) may transform and density thePMX layer to form a denser layer. For example, a first beam (e.g., 1612)may form the PMX layer, and the second beam (e.g., 1621) may transformand density the PMX layer to form a denser layer. The first beam may bea type-1 energy beam. The second beam may be the type-2 energy beam. Thetype-2 energy beam may be a power density that is lower than that of thetype-1 energy beam (e.g., lower by at least 3 times (*), 4*, 5*, 6*, 7*,8*, 9*, 10*, 15*, or 20*). The type-2 energy beam may be focused ordefocused. The type-2 energy beam may have a larger cross section ascompared to the type-1 energy beam (e.g., larger by at least 2 times(*), 3*, 4*, 5*, 6*, 7*, 8*, 9*, 10*, 15*, or 20*). During the PMX (set)densification process, the type-2 energy beam may have dwell time (e.g.,to form a tile) of about 250 milliseconds (msec), 500 msec, 1.0 second(sec), 1.5 sec, 2.0 sec, 2.5 sec, 3.0 sec, or 5.0 sec. During the PMX(set) densification process, the type-2 energy beam may have dwell timebetween any of the afore-mentioned dwell times (e.g., from about 250msec to about 5.0 sec, from about 500 msec to about 3.0 sec, or fromabout 1.0 sec to about 3.0 sec). The PMX layer set may comprise one ormore intervening pre-transformed material layers (e.g., FIG. 8A, 803).The PMX set may be used to vertically extend (e.g., thicken) a bottomskin layer (e.g., of an overhang and/or cavity ceiling structure (e.g.,FIG. 30A-30E)). The PMX set used for thickening may similarly compriseone or more intervening pre-transformed material layers. At least two ofthe plurality of intervening pre-transformed material layers may beseparated by PMX layers. At least two of the plurality of interveningpre-transformed material layers may contact each other. The PMX layerset comprising the intervening one or more layers of pre-transformedmaterial, may be densified in one densification process (e.g., FIG.30D). Thickening a bottom skin (e.g., of an overhang and/or cavityceiling) may comprise one or more cycles of forming PMX layer (set)density* it, and forming a subsequent PMX layer (set). In someembodiments, the PMX layers can be used to vertically extend any of the3D printed sections of the 3D object described herein (e.g., therigid-portion, and/or a densified layer).

At times, it is desirable to form a shallow angled (e.g., complex)structure (e.g., overhang structure) with a low degree of deformation(e.g., no substantial deformation). Substantial may be relative to theintended purpose of the 3D object. The shallow angled structure may begenerated by (i) forming a porous matrix layer (e.g., or PMX layer set)that assumes at least a portion of the shallow angled structure. (ii)optionally supplementing the material of the PMX layer (set) by addingpre-transformed material that penetrates into the PMX layer (set) (iii)densifying at least a portion of the PMX layer (set) by transforming it(and optional added pre-transformed material within) with a transformingenergy beam, and (iv) optionally repeating operations (i) to (ii). Thetransformation of the PMX layer (set) may be using the type-2 energybeam (e.g., to form deep, shallow, and/or hemispherical tiles), and/ortype-1 energy beam. At least portion of the (e.g., shallow angled) PMXstructure may be densified in operation (iii) by generating anon-uniform thermal profile along the forming (e.g., shallow angled) tobe densified structure. The non-uniform thermal profile may becontrolled (e.g., in real time). The control may be by a controller. Thecontrol may comprise altering at least one characteristic of the energybeam and/or energy source that generates the energy beam. For example, avelocity, cross section, and/or power density of the energy beam may bealtered such that the resulting temperature at the vulnerable portionwill be higher (or lower) as compared to adjacent positions. Forexample, a velocity, cross section, and/or power density of the energybeam may be altered such that the resulting temperature at a positionaway from an edge tip and/or rigid-portion will be higher or lower. Theedge may connect the (e.g., shallow) angled structure to a bulkerportion of the 3D object. The higher temperature may be generated byusing a denser path scheme (e.g., dense hatching) along which the energybeam travels (e.g., denser hatching). In some embodiments, the distancebetween paths of the energy beam (e.g., hatches) may be (e.g.,substantially) identical. At times, the distance between the paths maybe varied. The variation may follow a pattern. The pattern may be linear(e.g., the variation may be linear). At times, the density of thehatches may be of (e.g., substantially) constant. At times, the densityof the hatches may be varied. The higher temperature may be generated byincreasing the dwell time of the energy beam in the portion of the(e.g., shallow) angled structure closer to the edge, and/orrigid-portion. The angled structure can have an acute or obtuse anglewith respect to a balker portion of the 3D object, the platform, or adirection perpendicular to the platform. The angled structure may have ashallow, intermediate, or steep angle with respect to a bulker portionof the 3D object, the platform, or a direction perpendicular to theplatform. Velocity profile of the energy radiation may be variable(e.g., in real time during the densification of at least a portion ofthe shallow angled PMX matrix). At times, the energy beam may travel ata speed comprising a constant speed or a varied speed. At times, whenthe velocity profile is at a constant speed, the power profile may bevaried. The choice of energy beam characteristic (e.g., temperature,dwell time, and/or delay time) may relate to the angle of the complex(e.g., overhang or ceiling) structure. For example, for a shallow angle3D structure (e.g., ledge), it may be desirable to shorten the amount oftime for solidification of a melt pool (i.e., shorten the time that themelt pool remains molten, e.g., to prevent balling and/or drooping). Forexample, for a steeper angle complex structure (e.g., blade), it may bedesirable to prolong the amount of time for solidification of a meltpool (i.e., prolong the time that the melt pool remains molten, e.g., toallow wetting of the bottom skin). A low power density, and/or shortdwell times may be used to shorten the amount of time for solidificationof a forming melt pool. A high-power density, and/or long dwell timesmay be used to prolong the amount of time for solidification of aforming melt pool. To prolong the time for solidification, an elongatedenergy beam, and/or a dithering (e.g., retro-scan) energy beam may beused. At times, a low power density energy beam e,g type-2 energy beam)may be used having a higher dwell time to prolong the time forsolidification. At times, the material bed may not be heated during atleast a portion of the 3D printing (e.g., during the transforming). Attimes, the material bed may be at an ambient temperature during at leasta portion of the 3D printing (e.g., during the transforming).

In some embodiments, the transforming energy beam forms more than onemelt pool by transforming at least a portion of the pre-transformedmaterial to a liquid state. The melt pools may be successively formed.The melt pools may contact one another in at least one point. Theplurality of melt pools may be fluidly connected such that a first fluidfrom a first melt pool may aggregate with a second fluid of a secondmelt pool that is directly adjacent to the first melt pool. In someexamples, at least a portion of the material within a plurality of meltpools is retained in a liquid state. In some embodiments, the amount ofaggregated liquid material in one or more melt pools may be controlled(e.g., in real time, e.g., by a controller). The controller may controlat least one characteristic of the transforming energy beam and/orenergy source that generates it, to effectuate control of the liquidmaterial in the one or more melt pools. Effectuate may comprisecontrolling the temperature (e.g., over a time period) of the one ormore melt pools. In some embodiments, the number of melt pools in whichat least a portion of the material is in a liquid state, is controlled(e.g., by a controller, in real time, for example, by controlling atleast one characteristic of the transforming energy beam and/or theenergy source that generates it). In an example, a first melt pool thatcomprises a first liquid material is formed: and subsequently a secondmelt pool that is directly adjacent to the first melt pool is formedbefore the first liquid material completely hardens (e.g., solidifies),which second melt pool comprises a second liquid material. For example,a second melt pool, adjacent to a first melt pool may be formed whilethe first melt pool contains at least some material that is in a liquidstate (e.g., molten). The liquid, material in the plurality ofcontacting melt pools may aggregate (e.g., over the time period).Aggregation (e.g., coming together) of the liquid material (e.g., fromoverlapping and/or combined melt pools), may form undesired features.The undesired features may affect the appearance and/or (e.g., intended)function of the 3D object. At times, an accumulated (e.g., large) volumeof liquid (e.g., molten) material within the forming structure may ballup, and/or drip down from the forming 3D structure. The liquid materialmay be a liquid volume from at least about 4, 5, 6, 7, 8, 9, or 10 meltpools, depending on the type of pre-transformed material used. Theliquid material may be a liquid volume from a melt pool area having alength of at least about 4, 5, 6, 7, 8, 9, or 10 melt pool diameters,depending on the type of pre-transformed material used. The ballingand/or dripping (e.g., forming droops) may form the undesiredfeature(s). For example, the aggregation of liquid may result infragmentation of the overhang structure and/or roughen the surface(e.g., bottom exposed surface) of the forming 3D structure. The overallvolume of the liquid material in the one or more melt pools (e.g.,plurality of melt pools) may be controlled (e.g., in real time, e.g., bya controller). The control may be to curb (e.g., avoid) the undesiredfeatures (e.g., balling and/or drooping effects). FIG. 25A shows a sideview example of one or more melt pools (e.g., 2510). In someembodiments, wetting of the bottom skin surface of a forming 3D objectmay be desired (e.g., to reduce a roughness of the bottom skin surface).In some embodiments, a controller may control the number of melt poolsthat at least partially retain liquid material to (i) allow wetting ofthe bottom surface to a (e.g., desired and/or predetermined) degree,(ii) curb appearance of the undesired features, or any combinationthereof (e.g., to allow wetting of the bottom surface to a (e.g.,desired and/or predetermined) degree and curb appearance of theundesired features). In some embodiments, a balance is found betweenhaving sufficient liquid to wet the bottom surface of the forming 3Dobject, which volume is insufficient to form the undesired features(e.g., at least to the extent that obstructs and/or disturbs theintended purpose of the 3D object). For example, the controller maymaintain an area having a length of at most about one, two, three, four,five or six melt pool diameters (e.g., 2520, comprising d₁, d₂, and d₃)such that all the melt pools in that area will at least partially remainin a liquid state, when forming the layer (e.g., 2525) as part of the 3Dobject. The controller may maintain an area having a length of at leastabout one, two, three, four, five or six melt pool diameters, such thatall the melt pools in that area will at least partially remain in aliquid state, when forming the layer as part of the 3D object. Thecontroller may maintain an area having a length between any of theafore-mentioned length (e.g., from one diameter to six diameters, orfrom two diameters to five diameters), such that all the melt pools inthat area will at least partially remain in a liquid state, when formingthe layer as part of the 3D object. The controller may maintain an areacomprising at most about one, two, three, four, five or six melt pools,such that all those melt pools will at least partially remain in aliquid state, when forming the layer as part of the 3D object. Thecontroller may maintain an area comprising at least about one, two,three, four, five or six melt pools, such that all those melt pools willat least partially remain in a liquid state, when forming the layer aspart of the 3D object. The controller may maintain an area comprising anumber of melt pools between any of the afore-mentioned number of meltpools (e.g., from one melt pool to six melt pools, or from two meltpools to five melt pools), such that all the melt pools in that areawill at least partially remain in a liquid state, when forming the layeras part of the 3D object. The liquid material may be accumulated from anarea having a width of about one melt pool. The at least partiallyliquid area may comprise a height (FIG. 25A, “h”) of about one meltpool. The length of the at least partially liquid area may comprise anactual number of melt pools that exceeds its number of melt pooldiameter length, when the melt pools partially overlap each other. Thelength of the at least partially molten area that spans a certain numberof melt pool diameters (e.g., three melt pool diameters in 2520), maycomprise more than three melt pools that partially overlap each other(e.g., four melt pools comprising 2522). In FIG. 25A, the black meltpools in 2525 illustrate hardened melt pools that do not comprisematerial in a liquid state, whereas the gray melt pools in 2522 at leastpartially comprise material in a liquid state. The gray shades representthe order in which the melt pools were formed, with the lighter graybeing the most recent melt pool (e.g., 2510), and the darker gray beingpreviously formed melt pools. The melt pools in the example shown inFIG. 25A were formed along the trajectory 2530 as viewed from the side.FIG. 25B shows a schematic example of controlling a temperature 2590 ofthree melt pools (e.g., which three melt pools correspond to graphs2440, 2442 and 2444) as a function of time 2585. The control maycomprise controlling at least one characteristic of the transformingenergy beam and/or of the energy source that generates the transformingenergy beam. The temperature control may affect (e.g., control) theamount (e.g., volume) of liquid (e.g., molten) material in those meltpools. FIG. 25B shows an example of a first temperature profile (e.g.,2546) of a first melt pool that was formed at t₁ (e.g., melt pool 2507of FIG. 25A), wherein during a time period shown in 2585 (e.g., fromtime #1 to time #2), the first melt pool experiences a (e.g., narrow)temperature distribution that fluctuates around T₃ (e.g., above and/orbelow (e.g., T₃), wherein T₂ is below (e.g., colder than) T_(m). Attimes, although the fluctuations of the temperature (e.g., as measuredfrom the exposed surface of the melt pool) do not reach and/or exceed amelting temperature (T_(m)) of the material from which it is composed(e.g., and hence the first time period in which the measured temperaturereach and/or exceed a T_(m), equals zero), some material in the meltpool remains in a liquid state. FIG. 25B shows an example of a secondtemperature profile (e.g., 2544) of a second melt pool that was formedat t₂ (e.g., melt pool 2508 of FIG. 25A), wherein during a time periodshown in 2585, the second melt pool experiences a (e.g., narrow)temperature distribution that fluctuates around T₂ (e.g., above, and/orbelow (e.g., T₂), wherein T₂ is below (e.g., colder than) T_(m). Attimes, the fluctuations of the temperature reach and/or (e.g., slightly)exceed a melting temperature (T_(m)) of the material from which it iscomposed. During a second time period in which the fluctuatingtemperature reaches and/or exceeds the inciting temperature, a portionof a solid material within the second melt pool may melt, and/or amolten material in the second melt pool may remain molten. FIG. 25Bshows an example of a third temperature profile (e.g., 2542) of a thirdmelt pool that was formed at t₂ (e.g., melt pool 2509 of FIG. 25A),wherein during a time period shown in 2585, the third melt poolexperiences a (e.g., narrow) temperature distribution that fluctuatesaround T₁ (e.g., above, and/or below (e.g., T₁), wherein T₁ is below(e.g., colder than) T_(m). At times, the fluctuations of the temperaturereach and/or exceed a melting temperature (T_(m)) of the material fromwhich it is composed during a time period that is greater as compared tothe second melt pool. During a third time period in which thefluctuating temperature reaches and/or exceeds the melting temperature,a portion of a solid material within the third melt pool may melt,and/or a molten material in the third melt pool may remain molten. Thethird time period is greater than the second time period. FIG. 25B showsan example of a fourth temperature profile (e.g., 2540) of a fourth meltpool that was formed at t₄ (e.g., melt pool 2510 of FIG. 25A), whereinduring a time period shown in 2585, the fourth melt pool experiences a(e.g., narrow) temperature distribution that fluctuates around T_(m)(e.g., above, and/or below (e.g., T_(m)), wherein T_(m) is the meltingtemperature of the material from which the melt pool is formed. During afourth time period in which the fluctuating temperature reaches and/orexceeds the melting temperature, a portion of a solid material withinthe fourth melt pool may melt, and/or a molten material in the fourthmelt pool may remain molten. The fourth time period is greater than thethird time period. The time t₁ is before t₂ that is before t₃ that isbefore t₄. The temperature T₃ is colder than T₂ that is colder than T₁that is colder than T_(m). The temperature may be assessed utilizingdetector/sensor measurements of the target surface (e.g., of an exposedsurface of the melt pools). Retaining the temperature range may comprisetemperature fluctuations over time (e.g., as depicted in 2544). Thetemperature fluctuations can be homogenous (e.g., as in FIG. 25B) ornon-homogenous.

At times, the 3D structure is printed without any auxiliary supportsother than the one or more rigid-portions (which are part of the 3Dobject). The printing methodology may comprise (i) forming a porousmatrix (e.g., set), (ii) densifying the area enclosed by the porousmatrix (e.g., using a transformation operation), and (iii) optionallyrepeating s (i) to (ii) to increase the height (e.g., thickness) of theoverhang. The 3D structures (e.g., overhangs) may have a shallow angle(e.g., with respect to the platform and/or exposed surface of thematerial bed). In some instances, the rigid-portion may constrain thehardening complex structure. At times, these structural constraints willform one or more deformations (e.g., defects, e.g., structural defects)in a hanging structure and/or cavity that extends from therigid-portion. The deformations may comprise cracks or breaking points.The process(es) described herein may allow reducing the deformation atleast in the overhang (e.g., cavity bottom and/or ceiling cavity) thatconnect to the rigid-structure(s). The process may comprise creating abottom skin layer that may or may not be connected to one or morerigid-portions. The bottom skin layer may comprise a PMX or a densermaterial as compared to the PMX. The process may comprise creating a(e.g., PMX) bottom skin layer that may or may not be connected to one ormore rigid-portions. The bottom skin layer can be created using thetype-1 energy beam and/or type-2 energy beams. The bottom skin layer maybe formed using hatching and/or tiling. The hatches may be a sectoralhatch. The tiling may be along a tiling path. The tiling path may be asectoral path. The one or more rigid-portions may be anchored to aplatform, or may be floating anchorlessly in the material bed. In someexamples, an angle is formed between the vector (e.g., hatch, or path-of-tiles) and the growth direction of the bottom skin layer. Thedirection of the hatch/path vector may be (e.g., substantially)perpendicular to the growth direction of the forming bottom skin layer.The hatch/path vector may correspond to at least a portion of the bottomskin layer. In some embodiments, the requested overhang (e.g., 922) aspart of the 3D object forms an angle (e.g., 925) with the rigid-portion(e.g., 920). Formation of the angular structure may be effectuated bydepositing successive layers that are offset with respect to each otherin the direction of the overhang (e.g., ceiling) growth, whichsuccessive layers connect to (e.g., and partially overlap with) eachother. FIGS. 17A-17F illustrate example operations in forming anoverhang structure by performing the STO process, wherein the overhangstructure is connected to a rigid-portion. FIG. 17A shows an example ofa material bed (e.g., 1705) disposed on a platform (e.g., 1715) thatcomprises pre-transformed material. A portion of the material bed may beirradiated (e.g., and transformed) using a transforming energy beam(e.g., 1720) to form a rigid-portion (e.g., 1710). In the example shownin FIG. 17A, the rigid structure contacts the platform. Therigid-portion may provide support for forming the overhang structure.The overhang may contact, connect, and/or be anchored to therigid-portion. FIG. 17B shows an example of dispensing a (e.g., planar)layer of pre-transformed material (e.g., 1725) above the rigid-portione.g., 1722) disposed in the material bed. FIG. 17C illustrates anoperation of irradiating (e.g., and transforming, e.g., sintering, ormelting) a portion of the pre-transformed material layer that contactsthe rigid-portion (e.g., and is above the rigid-portion), by using atransforming energy beam (e.g., 1730) to form a portion of the overhangstructure (e.g., 1735). Transforming may include generating one or moremelt pools. FIG. 13C shows an example of forming one or more melt pools(e.g., 1735) when transforming a portion of the material bed (e.g.,1733) with the transforming energy beam. At least one melt pool (e.g.,1731) may (e.g., horizontally) exceed the rigid-portion. In someembodiments, a row of melt pools may be formed to form a horizontalextension of the rigid-portion in at least one horizontal direction. Oneor more melt pool in the row of melt pools may connect to and/or overlapthe rigid-portion. For example, the row of melt pools may connect toand/or overlap the rigid-portion in at least one position. For example,the row of melt pools may connect to and/or overlap at least a portionof the rigid portion rim. FIG. 13C shows an example of a vertical crosssection of a melt pool 1731 that horizontally extends beyond the rigidportion 1732, and melt pools that connect to the overhanging melt pool1731, and overlap the rigid portion (e.g., 1735). The transformingenergy beam may be a type-2 energy beam and/or a type-1 energy beam. Thetype-2 energy beam may be a power density (e.g., at the target surface)that is lower than that of the type-1 energy beam (e.g., lower by atleast 3 times (*), 4*, 5*, 6*, 7*, 8*, 9*, 10*, 15*, or 20*). The type-2energy beam may be focused or defocused (e.g., at the target surface).The type-2 energy beam may have a larger cross section as compared tothe type-1 energy beam (e.g., larger by at least 2 times (*), 3*, 4*,5*, 6*, 7*, 8*, 9*, 10*, 15*, or 20*). During the STO process, thetype-2 energy beam may have dwell time (e.g., at the target surface) ofabout 1 milliseconds (msec), 5 msec, 10 msec, 15 msec, 20 msec, 30 msec,or 50 msec. During the STO process, the type-2 energy beam may havedwell time (e.g., at the target surface) between any of theafore-mentioned dwell times (e.g., from about 1 msec to about 50 msec,from about 5 msec to about 30 msec, from about 10 msec to about 20 msec,or from about 10 msec to about 50 msec). The transforming energy beammay be (e.g., substantially) circular or elongated. The transformingenergy beam may operate in retro-scan mode. In some embodiments, aportion of the rigid structure is extended concurrently with forming theoverhang. The extension of the rigid portion may be using any of the 3Dprinting methodologies described herein (e.g., forming a dense layer, orforming a PMX layer that is subsequently densified). FIG. 17D shows anexample of the first transformed layer (e.g., hardened layer, 1740) thatis part of an overhang structure that is connected to the rigid-portion.The first transformed may comprise material that is denser than arespective volume containing the pre-transformed material. The firsttransformed layer of the overhang structure may he at an angle (e.g.,shallow angle) with respect to the platform and/or exposed surface ofthe material bed. The angled overhang structure can have an acute orobtuse angle with respect to a bulker portion of the 3D object, theplatform, or a direction perpendicular to the platform. The angledoverhang structure may have a shallow, intermediate, or steep angle withrespect to a bulker portion of the 3D object, the platform, or adirection perpendicular to the platform. For example, the firsttransformed material may be (e.g., substantially) parallel to theplatform and/or exposed surface of the material bed. FIG. 17E shows anexample of dispensing a second layer of pre-transformed material (e.g.,1745) adjacent to (e.g., above) the previously layer (e.g., 1748) oftransformed material as part of the overhang structure. The second layerof pre-transformed material may be irradiated (e.g., and transformed,e.g., sintered, or melted) to form a second transformed (e.g., denser,and/or hardened) portion of the overhang structure. Transforming mayinclude irradiating at least a portion of the second pre-transformedmaterial layer, using a transforming energy beam. Transforming mayinclude re-melting the first transformed material layer (e.g., 1748)while forming the second layer (e.g., transforming at least a portion ofthe pre-transformed material layer, e.g., 1750). Transforming mayinclude generating one or more melt pools (e.g., 1750). The melt poolsmay be deep enough to melt through multiple layers (e.g., first andsecond layer). In order to elongate the resulting overhang (e.g., aspart of a ceiling), at a portion of one melt pool (e.g., horizontally)exceeds (e.g., 1743) the previously formed layer of transformed material(e.g., 1748). FIG. 17F shows an example of two (e.g., two) layers oftransformed material (e.g., 1750, 1755) of an overhang structure, thatare connected to a rigid-portion formed within the material bed, whichoverhang forms an angle beta (β) with the rigid-portion, and an anglealpha (α) with the exposed surface (e.g., 1751) of the material bed (andwith the platform 1752).

In some embodiments, the requested 3D object comprises a (e.g.,vertical) extension of the bottom skin layer, which bottom skin layer isof a first formed 3D object layer, of a ceiling and/or of an overhang.The vertical extension (e.g., thickening) of the bottom skin layer maybe done using any of the 3D printing methodologies disclosed herein. Forexample, the thickening of the bottom skin layer may comprise (i)forming at least one PMX layer above the bottom skin layer, (ii)dispensing one or more layers of pre-transformed material above thebottom skin layer, or (iii) any combination thereof. Subsequently, (i) atransforming energy beam may transform the PMX layer (set) to form adenser layer of transformed material as part of the 3D object, whichdenser layer contacts the bottom skin layer and at least verticallyextends at least a portion of it, (ii) a transforming energy beam maytransform the pre-transformed material layer (set) to form a layer oftransformed material as part of the 3D object, which layer oftransformed material contacts the bottom skin layer and verticallyextends at least a portion of it. The PMX layer may connect in at leastone position to the bottom skin layer. The newly transformed layer(e.g., originating from a PMX and/or a pre-transformed material) mayconnect in at least one position to the bottom skin layer. In someembodiments, the bottom skin layer is connected to a rigid-portion. ThePMX layer (set) and/or transformed material portions may connect to therigid-portion. In some examples, the bottom skin layer, PMX layer (set)and/or transformed material portions may connect to the rigid-portion.FIGS. 30A-30D show examples of operation for thickening a bottom skin ofan overhang structure that contacts a rigid-portion. The bottom skin maybe formed using any suitable method described herein. For example, thebottom skin layer be formed using STO or MTO. In the examples shown inFIGS. 30A-30D, the overhang bottom skin layer is thickened using a PMXlayer set. In some examples, the overhang bottom skin layer is thickenedusing a PMX layer only in part. In some examples, the overhang bottomskin layer is thickened using a single step transformation in which apre-transformed material is transformed to form a transformed materialthat (e.g., subsequently) forms a hardened material that is sufficientlydense (e.g., per a requested and/or predetermined density). FIG. 30Ashows an example of a material bed 3012 that comprises a rigid portion3018 and a first bottom skin layer 3010 as part of an overhang structurethat contacts the rigid-portion 3018, as well as a first PMX layerportion 3005 located above the rigid-structure 3018 and next to thefirst bottom skin layer 3010. The overhang structure may be formed byany method described herein (e.g., STO). The first PMX layer may betransformed prior to deposition of a subsequent layer of pre-transformed material and/or prior to formation of a third bottom skinlayer as an extension of the bottom skin of the overhang. In someexamples, at least two of the thickening layers (e.g., PMX orpre-transformed material) are transformed individually (e.g., prior toeach deposition of a new layer of pre-transformed material), forexample, transformed one by one. In some examples, at least two of thethickening layers (e.g., PMX or pre-transformed material) aretransformed collectively as a set, for example, transformed together(e.g., using deep tiling). The rigid-portion (e.g., 3018) may provide ananchor or a support for (i) the bottom skin layer, (ii) the formingoverhang structure (e.g., that includes a thickened bottom skin layer),and/or for (iii) the layer portion that thickens the bottom skin layer.

FIG. 30B shows an example of vertically elongating (e.g., thickening)the first formed overhang bottom skin layer 3028 and the rigid-portion3029 by fabricating a second bottom skin layer 3020 that that partiallyoverlaps the first bottom skin layer 3028, wherein the non-overlappingportion of the second bottom skin extends in the direction of overhangextension 3021 vertically elongating (e.g., thickening) a portion of thefirst bottom skin overhang by fabricating a second PMX layer portion3025 above that portion of the first bottom skin layer, and verticallyelongating the rigid-portion by laterally extending the second PMX layerportion 3025 to above 3027 the rigid-portion 3029. In some examples, thefirst PMX layer may be densified (e.g., by transformation), prior toformation of the second PMX layer. In the example shown in FIG. 30B, thefirst PMX layer was not transformed to form a denser layer portion,prior to formation of the second PMX layer. The first and second PMXlayers form a PMX layer set. The PMX layer set may be transformed priorto deposition of a subsequent layer of pre-transformed material and/orprior to formation of a third bottom skin layer as an extension of thebottom skin of the overhang. At times, the PMX structure may be provided(e.g., laterally) adjacent to a bottom skin layer. For example, the PMXlayer (e.g., 3025) may be formed laterally adjacent to the second bottomskin layer (e.g., 3020). At times, the PMX structure may be providedadjacent to (e.g., above) an overhang structure. For example, the PMXlayer (e.g., 3025) may be formed above the first overhang structure(e.g., 3028). At times, the PMX structure (e.g., 3035) may be providedadjacent to (e.g., laterally, and above) one or more overhangstructures. For example, the PMX structure e.g., 3035) may be formedabove the rigid-portion (e.g., 3029), the first overhang structure(e.g., 3031), the second overhang structure (e.g., 3028), and laterallyadjacent to the third overhang structure (e.g., 3032). At times, the PMXstructure (e.g., 3035) may be supplemented (e.g., filled) withpre-transformed material prior to its densification (e.g., bytransforming it using the transforming energy beam).

FIG. 30C shows an example of further extending the overhang by forming athird bottom skin layer portion 3032, and thickening the previouslyformed first bottom skin layer 3031 and second bottoms skin layer 3038,by forming a PMX layer 3035 that also serves to vertically elongate therigid structure 3039. When extending the 3D object, various portions ofa previously formed layer of the 3D object may be extended using one ormore 3D printing methodologies (e.g., as described here). In someembodiments, the bottom skin layers are vertically elongated (e.g.,thickened) by a PMX layer, while the rigid structure is elongated in aprocess that does not use a PMX layer. In some embodiments, the bottomskin layers are vertically elongated (e.g., thickened) with a PMX layerprecursor, while the rigid structure is vertically elongated using asingle transformation (STO) process (e.g., using hatching and/ortiling). The transforming energy beam may transform one or more PMXlayers. For example, the transforming energy beam may transform aplurality of PMX layers in a single irradiation procedure. In someexamples, the transforming energy beam may transform one or more layersthat form at least a portion of the overhang structure. The one or morelayers may be of PMX or of a higher material density. The transformingenergy beam. (e.g., 3045) may form a melt pool (e.g., 3040). The meltpool may have a low aspect ratio, high aspect ratio, or behemispherical. At times, the melt pool may transform (e.g., re-melt,re-transform) multiple layers (e.g., that form at least a portion of the(e.g., the entire) PMX structure. While transforming the material thatvertically extends the bottom skin layers, the transforming energy beammay also re-transformed at least a portion of the bottom skin layers.FIG. 30D shows an example of a melt pool 3040 that penetrates through aplurality of PMX layers, and transforms a portion of those layers. FIG.30E shows an example in which the transformed material forms a part of avertical extension portion 3055 of a ledge as part of the 3D object.

In some embodiments, at least a portion of the 3D object may be formedusing at least one PMX layer (e.g., as a precursor, or as the requested3D object). In some embodiments, a bottom skin layer is formed using aPMX layer (e.g., as a precursor). At times, a rigid portion may beformed using a porous matrix structure. At times, a 3D object thatcomprises a functionally graded material may be formed using the porousmatrix structure. The functionally graded 3D object may comprise atleast two portions that differ in their microstructure. Themicrostructure may comprise grain orientation, material density, degreeof compound segregation to grain boundaries, degree of elementsegregation to grain boundaries, material phase, metallurgical phase,material porosity, crystal phase, crystal structure, or material type.The various portions may be made by fabricating at least two differentPMX precursors that facilitate the at least two portions of the 3Dobject respectively, which two different portions differ in theirmicrostructures. For example, the PMX structure may comprise one or moreporous layers with different densities, pore morphologies, pore specialarrangements, and/or material of the PMX portions. The at least twodifferent portions may be at least two different PMX layers, and/or twodifferent portions of the same PMX layer. The at least two PMX layersmay differ in their FLS (e.g., their layer thickness (e.g., height)).FIGS. 19A-19F shows an example of forming a thickened bottom skin layerthat is disposed anchorlessly in a material bed above a platform, usinga porous matrix structure. FIG. 19A show an example of a material bed(e.g., 1900) that comprises pre-transformed material, disposed above aplatform (e.g., 1905). FIG. 19B shows an example of irradiating (e.g.,and transforming) a portion of the pre-transformed material within thematerial bed using a transforming energy beam (e,g, 1910). Thepre-transformed material may be transformed to form a first porous layer(e.g., 1915) having a first microstructure. The amount of porositywithin the first porous layer may be controlled (e.g., in real time,e.g., using a controlled. Controlling may comprise adjusting at leastone characteristic of the transforming energy beam (e.g., power per unitarea) and/or of the energy source that generates it. FIG. 19C shows anexample of irradiating a portion of a second layer of pre-transformedmaterial that was disposed over the first porous layer (e.g., 1930), thetransforming energy beam (e.g., 1922). The pre-transformed material maybe transformed to form a second porous layer (e.g., 1925) using thetransforming energy beam. The second PMX layer may have the same or adifferent microstructure, as compared to the first PMX layer. Forexample, the second PMX layer may comprise a different amount ofporosity than the first PMX layer. FIG. 19D shows an example ofirradiating a portion of a third layer of pre-transformed material thatwas dispensed over the previously formed PMX layers (e.g., 1935, 1940).At least a portion of the pre-transformed material in the third layermay be transformed to form a third PMX layer (e.g., 1945), using atransforming energy beam (e.g., 1947). The third porous layer may have adifferent microstructure (e.g., amount, distribution, and/or arrangementof porosity) than the first porous layer and/or the second porous layer.The combination of the multiple PMX layers may be referred to as the PMXlayer set. At times, the PMX layer set may be supplemented withpre-transformed material (e.g., that fill one or more pores within theporous matrix) after its formation, and before its densification. FIG.19E shows an example of transforming (e.g., densifying) a plurality ofPMX layers, by projecting a transforming energy beam (e.g., 1951) thatgenerates one or more melt pools (e.g., 1950). Transforming may comprisemelting through the entire PMX layer set (e.g., three PMX layers).Transforming may comprise melting through the PMX layer set until atleast a portion of the bottom surface of the PMX layer set plasticallyyields, transforms, wets densities, or any combination thereof. FIG. 19Fshows an example of a transformed structure (e.g., densified, 1955) thatis anchorlessly suspended in the material bed, which layers forming thetransformed structure may be denser (e.g., and denser) than theirrespective MIX layers that served as its precursor. The plurality ofdenser layers may be substantially identical or may differ. In someembodiments, the densification of the PMX layer set results in a singlethick layer of transformed material. The layers of PMX that served as aprecursor to the thick may be (e.g., immediately) apparent. It someembodiments, it may not be (e.g., immediately) apparent that severallayers sewed as a precursor to the thick transformed material layer.

At times, the forming 3D object comprises a complex geometry (e.g.,fine, intricate structures). For example, the complex geometry mayinclude thin wedge, (e.g., shallow) angled structure, small horizontalcross sectional structure, and/or a thin ledge connector. Thetransforming energy beam (e.g., the type-2 energy beam) may have afootprint that is wider than the fundamental length scale (FLS, i.e.,length, height, width, or diameter) of the complex geometry. In someembodiments, to form the complex geometry structure, the printingmethodology comprises generating a transformed material by forming ahigh aspect ratio melt pool. The high aspect ratio melt pool maypenetrate one or more layers. The one or more layers may comprise a PMXlayer (set), a dense(r) 3D object portion, or a pre-transformed materiallayer. The high aspect ratio melt pool may be formed with an energy beamthat has a footprint sufficiently narrow to form the intricatestructure. The high aspect ratio melt pool may be formed with an energybeam that has a sufficient power density to form the high aspect ratiomelt pool. In some embodiments, the high aspect ratio melt pool may beelongated (e.g., expanding laterally the amount of transformed materialthat is a part of the melt pool). The elongation may be effectuated atleast in part by moving the transforming energy beam. At times, gas istrapped in the high aspect ratio melt pool. Prior to moving away fromthe high aspect ratio melt pool, the power density of the energy beammay be lowered during the final stages the high aspect ratio melt poolformation. Lowering the power density of the energy beam may alter(e.g., lower) the amount of gas trapping within the melt pool. In someembodiments, a portion of the forming 3D object includes fine, intricatestructures (e.g., at shallow angles). FIG. 26A shows a top view exampleof 3D object portions comprising intricate structures (e.g., 2605). Anenergy beam (e.g., 2602) with a narrow footprint (e.g., 2603) may beused to densify the fine portion(s) of the forming 3D object (e.g., whena PMX layer (set) is used as its precursor). The narrow footprinted(e.g., 2603) energy beam (e.g., 2602) may have a beam cross section thatis smaller than the beam cross section of the type-2 energy beam. Thenarrow footprinted energy beam may have a footprint on the targetsurface that is smaller than the footprint (e.g., 2604) of the type-2energy beam (e.g., 2601) that is formed on that target surface (e.g.,exposed surface of the material bed). FIG. 26B shows an example offorming high aspect ratio melt pools (e.g., 2610), viewed as a verticalcross section of the intricate structure (e.g., 2605). The high aspectratio melt pool may be formed using a transforming energy beam. Thetransforming energy beam (e.g., 2615) may comprise a high energydensity, and/or a small cross section. The energy beam may be focused ordefocused. The energy beam may have a cross section area that may be atmost equal to the horizontal cross sectional area of the finer structurearea (e.g., 2605). The transforming energy beam may form a high aspectratio melt pool (e.g., 2610), by irradiating the portion of the targetsurface. The target surface may comprise a pre-transformed material, ora transformed material (e.g., a PMX layer (set)). At times, the complexportion of the 3D object may be formed by performing the HARMP process.FIGS. 29A-29E show an example of forming a fine portion of a 3D objectby forming HARMP, shown as a vertical cross section of the fine portion.FIG. 29A shows an example of a target surface 2900 (e.g., exposedsurface of a material bed, or of a PMX layer (set)e.g., 2905). FIG. 29Bshows an example of irradiating a portion of the target surface (e.g.,2912) using a transforming energy beam (e.g., 2910). The transformingenergy beam may irradiate at a position (e.g., 2915) on the targetsurface in a (e.g., substantially) stationary mariner. The transformingenergy beam may be configured to form a HARMP. FIG. 29C shows an exampleof forming a HARMP (e.g., 2920) with a depth of “d”. The HARMP mayextend to a desired depth (e.g., up to a depth “d”). The desired depthmay be a bottom of the MIX layer (set). The transforming energy beam maycause (e.g., 2932, 2934) a portion of the material to exit the HARMPvolume during its formation. The exiting material may comprise vapor,plasma, and/or other forms of sputtered (e.g., liquid, e,g., molten)material. The exiting material may form a HARMP well (e.g., a cavitywith an opening, e.g., 2925). The HARMP well may be formed within atleast a portion of the HARMP. At times, optionally, the HARMP well maybe elongated in a lateral direction (e.g., to increase the amount oftransformed material in a lateral direction), by moving the transformingenergy beam in a lateral direction. The HARMP well may be closed to forma melt pool. The melt pool may comprise one or more pores. The positionand/or number of pores may be controlled (e.g., in real time, e.g.,using a controller). The controller may control at least onecharacteristic of the energy beam and/or the energy source thatgenerates it. In some instances, the melt pool comprises (e.g., onaverage) a low porosity percentage. In some instances, the melt poolcomprises (e.g., substantially) no (e.g., detectable) pores. FIG. 29Dshows an example of closing of a HARMP well (e.g., 2920) to form themelt pool (e.g., 2950). The closing may comprise reducing (e.g.,gradually) an intensity of the transforming energy beam (e.g., 2945).The intensity reduction may include reducing the power per unit area ofthe energy beam. Reducing the intensity of the energy beam may includeadjusting one or more optical elements of an optical system or anastigmatism system. Reducing the intensity of the energy beam mayinclude adjusting one or more characteristics of the energy beamcomprising its power profile over time, or its pulsation scheme.Reducing the intensity of the energy beam may include adjusting one ormore characteristics of the energy source (e.g., its power). At times,the gradual intensity reduction of the transforming energy beam (e.g.,2945) may alter (e.g., reduce) its degree of penetration into the HARMP.A reduction of the energy beam penetration into the HARMP may allowliquid material to settle at the bottom of the HARMP and close the well(e.g., 2943). A reduction of the energy beam penetration into the HARMPmay reduce the amount of material that exits the HARMP during theirradiation of the energy beam, and thus reduce the size of the well(e.g., 2940). FIG. 29E shows an example of a transformed a resultingclosed HARMP that has hardened (e.g., 2950) The hardened HARMP maycomprise a low (e.g., diminished) number of pores.

In some embodiments, the formation of the HARMP utilizes pulse shapingof the transforming energy beam. In some embodiments, the formation ofthe HARMP utilizes a deviation from at least a portion of a steady powerpulse. The power density as a function of time, of transforming energybeam may comprise a plurality of segments (e.g., during a pulse). Theplurality of segments may comprise a power ramping up, a spike, aplateau, or a power ramping down. The pulse may be a dwell time of theenergy beam during which time it irradiates the target surface. FIG. 31Ashows an example of a steady pulse power (e.g., density) over time ofthe transforming energy beam that comprises a power (e.g., density) rampup (e.g., 3111), a power (e.g., density) plateau (e.g., 3112), a power(e.g., density) ramp down (e.g., 3113), and an intermission (e.g.,3114); wherein the ramp-down profile is linear. FIG. 31B shows anexample of a power (e.g., density) pulse profile over time of thetransforming energy beam in which the plateau and ramp down segments arealtered as compared to the steady pulse. In the example shown in FIG.31B, the plateau region (e.g., 3122) is shorter, and the ramp down time(e.g., 3123) is longer and has a non-linear descend. FIG. 31C shows anexample of a power e.g., density) pulse profile over time of thetransforming energy beam in which the ramp up, plateau, and ramp downsegments are altered as compared to the steady pulse. In the exampleshown in FIG. 31C, the ramp-up power (e.g., density) profile spikes to ahigher power (e.g., density) value, the plateau region is eliminated,and the ramp down time (e.g., 3123) is longer and includes a fast lineardescend (e.g., 3132) followed by a loner (e.g., gradual) non-lineardescend. The graphs shown in FIGS. 31A-31C may also represent the powerof the energy source that generates the energy beam, when the power ofthe energy source is represented as a function of time. The intermissionmay be referred to as a delay. Any one of the plurality of segments maybe controlled (e.g., modulated). At least two of the plurality ofsegments may be controlled (e.g., varied) collectively (e.g., in realtime, e.g., by a controller). At least two of the plurality of segmentsmay be controlled (e.g., varied) separately (e.g., in real time, e.g.,by a controller). For example, a pulse profile may comprise a ramp upwith a spike, followed by a plateau, and ending the pulse by a (e.g.,gradual) power ramping down. Controlling one or more of the plurality ofsegments may alter the percentage of pores (e.g., gas bubbles) in theHARMP upon its hardening (e.g., solidification).

In some embodiments, the position of the trapped gas and/or pore ischaracteristic of the power pulse profile over time that forms theHARMP. In some embodiments, at least one characteristic of the energybeam and/or power source that generates is, is altered during formationof the HARMP. In some embodiments, the power pulse profile over timethat forms the HARMP is manipulated to alter the position of the trappedgas and/or pore. At least two of the plurality of pulses may be (e.g.,substantially) identical during the formation of the HARMP. At least twoof the plurality of pulses may be (e.g., substantially) different duringthe formation of the HARMP. The difference may be in a pulse profile, ina characteristic of the energy beam (e.g., power density), and/or in acharacteristic of the energy source that generates it. In case theposition of the trapped gas and/or pore is disposed away from the lowertip of the HARMP, a plurality of pulses having progressively diminishingdepth may result in a reduction (e.g., elimination) of the trapped gasand/or pore in the HARMP. FIGS. 32A-D show examples of verticalcross-sectional views of a HARMP during its formation that comprisesthree successive energy beam pulses. FIG. 32A shows an example of aHARMP 3213 that was formed using a transforming energy beam, in whichHARMP a cavity 3210 is trapped. FIG. 32B shows an example of a HARMPthat was formed using two pulses that formed two melt pools with thefirst melt pool 3223 being deeper than the second (successive) melt pool3220, in which the cavity 3210 migrated to a higher position in which itis trapped. FIG. 32C shows an example of a HARMP that was formed usingthree pulses that formed three melt pools with the first melt pool 3233being deeper than the second (successive) melt pool 3230, which isdeeper than the third (successive) melt pool 3235, in which the cavity3232 migrated to a higher position in which it is no longer trapped.FIG. 32D shows an example of a HARMP 3240 that results from the processof FIGS. 32A-32C, which melt pool is a high aspect ratio melt pool thatis free of draped cavities.

In some embodiments, the energy beam irradiates a material andtransforms that material (e.g., to a fluid state, e.g., liquid state).In some embodiments, the energy beam is translated during formation of aHARMP. The energy beam may form a transformed material by irradiation(e.g., and generate a high aspect ratio melt pool) and subsequently movelaterally to elongate the melt pool in the direction of movement. Whenirradiating to initiate a melt pool formation (e.g., HARMP), a gas,plasma, or void may be formed (e.g., due to the elevated temperature inthe melt pool, e.g., at the position of maximum temperature). The voidmay form a pore upon hardening (e.g., abruptly), when the melt poolhardens without sufficient time for a fluidic transformed material toclose the void. To prevent pore formation, the energy beam mayfacilitate maintaining a fluid state in the melt pool for a sufficientlylong time for to allow closure of the void. For example, the energy beammay translate in a velocity that facilitates closure of the void by afluid transformed material. For example, the velocity of the energy beammay be a slow velocity. The lateral elongation of the melt pool may beat a velocity that facilitates closure of any pores. The HARMP may beformed using a spiraling (e.g., inward spiraling) or circling energybeam about an axis, which spiraling or circling facilitate a highertemperature at the center of the melt pool relative to its edges.

The hardened HARMP may be formed using one or more pulses that areseparated by one or more (respective) intermissions. During formation ofa HARMP the duration of at least two of the pulses forming it may be ondifferent time scales as at least two of the intermissions. Duringformation of a HARMP the duration of at least two of the pulses formingit may be on the same time scales as at least two of the intermissions.For example, a pulse and/or intermission of the transforming energy beamduring a HARMP formation may last at least about 0.5 milliseconds(msec). 1 ms, 5 ms, 10 msc, 30 msec, 50 msec, 100 msec, 500 msec, or1000 msec (e.g., along the path of HARMP melt pools). A pulse and/orintermission of the transforming energy beam during a HARMP formationmay last at most 1 ms, 5 ms, 10 msc, 30 msec, 50 msec, 100 msec, 500msec, or 1000 msec (e.g., alone, the path of HARMP melt pools). A pulseand/or intermission of the transforming energy beam during a HARMPformation may any time span between the afore-mentioned time values(e.g., from about 0.5 msec to about 1000 msec, from about 0.5 msec toabout 50 msec, from about 30 msec to about 500 msec, or from about 100msec to about 1000 msec), e.g., along the path of HARMP melt pools. TheHARMP may be generated from a pre-transformed material, a PMX, or adenser material than a PMX. The HARMP may be formed using a tiling ortype-1 energy beam. At least one characteristic of the energy beamforming the HARMP may be controlled by any controller or control schemedisclosed herein (e.g., real time control). The HARMP may be generatedby a type-1 energy beam and/or type-2 energy beam. The HARMP may begenerated by irradiating a transforming energy beam in one or morewelding modes. The welding modes may comprise a conduction mode, mixedmode (e.g., transition keyhole mode), penetration keyhole mode, and/ordrilling mode. For example, a plurality of pulses may be used to form aHARMP. At least two of the plurality of pulses may comprise the samewelding mode (e.g., penetration keyhole mode). At least two of theplurality of pulses may comprise the different welding modes (e.g., acombination of penetration keyhole mode and transition keyhole mode).

At times, the pre-transformed material (e.g., powder) is composed ofindividual particles. The individual particles can be spherical, oval,prismatic, cubic, wires, or irregularly shaped. The particles can have aFLS. The powder can be composed of a homogeneously shaped particlemixture such that all of the particles have substantially the same shapeand FLS magnitude within at most 1%, 5%, 8%, 10%, 15%, 20%, 25%. 30%,35%, 40%, 50%, 60%, or 70%, distribution of FLS. In some cases, thepowder can be a heterogeneous mixture such that the particles havevariable shape and/or FLS magnitude.

At times, the characteristics of the 3D object (e.g., hardened material)and/or any of its parts (e.g., layer of hardened material) is measuredby any of the following measurement methodologies. For example, the FLSvalues e.g., width, height uniformity, auxiliary support space, and orradius of curvature) of the layer of the 3D object and any of itscomponents (e.g., layer of hardened material) may be measured by an ofthe following measuring methodologies. The measurement methodologies maycomprise a microscopy method (e.g., any microscopy method describedherein). The measurement methodologies may comprise a coordinatemeasuring machine (CMM), measuring projector, vision measuring system,and/or a gauge. The gauge can be a gauge distometer (e.g., caliper). Thegauge can be a go-no-go gauge. The measurement methodologies maycomprise a caliper (e.g., Vernier caliper), positive lens,interferometer, or laser (e.g., tracker). The measurement methodologiesmay comprise a contact or by a non-contact method. The measurementmethodologies may comprise one or more sensors (e.g., optical sensorsand/or metrological sensors). The measurement methodologies may comprisea metrological measurement device (e.g., using metrological sensor(s)).The measurements may comprise a motor encoder (e.g., rotary, and/orlinear). The measurement methodologies may comprise using anelectromagnetic beam (e.g., visible or IR). The microscopy method maycomprise ultrasound or nuclear magnetic resonance. The microscopy methodmay comprise optical microscopy. The microscopy method may compriseelectromagnetic, electron, or proximal probe microscopy. The electronmicroscopy may comprise scanning, tunneling, X-ray photo-, or Augerelectron microscopy. The electromagnetic microscopy may compriseconfocal, stereoscope, or compound microscopy. The microscopy method maycomprise an inverted or non-inverted microscope. The proximal probemicroscopy may comprise atomic force, scanning tunneling microscopy, orany other microscopy method. The microscopy measurements may compriseusing an image analysis system. The measurements may be conducted atambient temperatures (e.g., R.T.), melting temperature e.g., of thepre-transfoimed material) or cryogenic temperatures.

In some embodiments, the microstructures (e.g., of melt pools) of the 3Dobject are measured by a microscopy method (e.g., any microscopy methoddescribed herein). The microstructures may be measured by a contact orby a non-contact method. The microstructures may be measured by using anelectromagnetic beam (e.g., visible or IR). The, microstructuremeasurements may comprise evaluating the dendritic arm spacing and/orthe secondary dendritic arm spacing (e.g., using microscopy). Themicroscopy measurements may comprise an image analysis system. Themeasurements may be conducted at ambient temperatures (e.g., R.T.),melting point temperature (e.g., of the pre-transformed material) orcryogenic temperatures.

In some embodiments, various distances relating to the chamber aremeasured using any of the following measurement techniques. Variousdistances within the chamber can be measured using any of themeasurement techniques. For example, the gap distance (e.g., from thecooling member to the exposed surface of the material bed) may bemeasured using any of the measurement techniques. The measurementstechniques may comprise interferometry and/or confocal chromaticmeasurements. The measurements techniques may comprise at least onemotor encoder (rotary, linear). The measurement techniques may compriseone or more sensors (e.g., optical sensors and/or metrological sensors).The measurement techniques may comprise at least one inductive sensor.The measurement techniques may include an electromagnetic beam (e.g.,visible or IR). The measurements may be conducted at ambienttemperatures (e.g., R.T.), melting temperature e.g., of thepre-transformed material) or cryogenic temperatures.

The methods described herein can provide surface uniformity across theexposed surface of the material bed such that portions of the exposedsurface that comprises the dispensed pre-transformed material, which areseparated from one another by a distance of from about 1 mm to about 10mm, have a vertical (e.g., height) deviation from about 100 μm to about5 μm. The methods described herein may achieve a deviation from a planaruniformity of the layer of pre-transformed material in at least oneplane (e.g., horizontal plane) of at most about 20%, 10%, 5%, 2%, 1% or0.5%, as compared to the average or mean plane (e.g., horizontal plane)created at the exposed surface of the material bed (e.g., top of amaterial bed) and/or as compared to the platform (e.g., buildingplatform). The vertical deviation can be measured by using one or moresensors (e.g., optical sensors).

At times, the 3D object has various surface roughness profiles, whichmay be suitable for various applications. The surface roughness may bethe deviations in the direction of the nominal vector of a real surface,from its ideal form. The surface roughness may be measured as thearithmetic average of the roughness profile (hereinafter “Ra”). Theprocess for forming 3D object may form 3D objects with a smooth bottomsurface (e.g., having a lower Ra value). The process for forming 3Dobject may form 3D objects with a smooth top surface (e.g., having alower Ra value). Smooth may include lower surface roughness values. Theprocess for forming 3D objects may be any process described herein. The3D object can have a Ra value of at least about 300 μm, 200 μm, 100 μm,75 μm, 50 μm, 45 μm, 40 μm, 35 μm, 30 μm, 25 μm, 20 μm, 15 μm, 10 μm, 7μm, 5 μm, 3 μm, 1 μm, 500 nm, 400 nm, 300 nm, 200 nm, 100 nm, 50 nm, 40nm, or 30 nm. The formed object can have a Ra value of at most about 300μm, 200 μm, 100 μm, 75 μm, 50 μm, 45 μm, 40 μm, 35 μm, 30 μm, 25 μm, 20μm, 15 μm, 10 μm, 7 μm, 5 μm, 3 μm, 1 μm, 500 nm, 400 mu, 300 nm, 200nm, 100 nm, 50 nm, 40 nm, or 30 nm. The 3D object can have a Ra valuebetween any of the aforementioned Ra values (e,g., from about 300 μm toabout 50 μm, from about 50 μm to about 5 μm, from about 5 μm to about300 nm, from about 300 nm to about 30 nm, or from about 300 μm to about30 nm). The Ra values may be measured by a contact or by a non-contactmethod. The Ra values may be measured by a roughness tester and/or by amicroscopy method (e.g., any microscopy method described herein). Themeasurements may be conducted at ambient temperatures (e.g., R.T.),melting point temperature (e.g., of the pre-transformed material) orcryogenic temperatures. The roughness may be measured by a contact or bya non-contact method. The roughness measurement may comprise one or moresensors (e.g., optical sensors). The roughness measurement may compriseusing a metrological measurement device (e.g., using metrologicalsensor(s)). The roughness may be measured using an electromagnetic beam(e.g., visible or IR).

In some embodiments, the 3D object is composed of successive layers ofsolid material that originated from a transformed material, andsubsequently hardened. For example, the 3D object may be composed ofsuccessive layers of solid material that originated from an at leastpartially molten material, and subsequently solidified. The successivelayers of solid material may correspond to successive cross sections ofa requested 3D object. The transformed material may connect (e.g., weld)to a hardened (e.g., solidified) material. The hardened material mayreside within the same layer as the transformed material, in anotherlayer (e.g., a previous layer). In some examples, the hardened materialcomprises disconnected parts of the three-dimensional object, that aresubsequently connected by newly transformed material. Transforming maycomprise fusing, binding or otherwise connecting the pre-transformedmaterial (e.g., connecting the particulate material). Fusing maycomprise sintering or melting.

In some embodiments, a cross section (e.g., vertical cross section) ofthe generated (i.e., formed) 3D object reveals a microstructure (e.g.,grain structure) indicative of a layered deposition. Without wishing tobe bound to theory, the microstructure (e.g., grain structure) may arisedue to the solidification of transformed (e.g., powder) material that istypical to anchor indicative of the 3D printing method. For example, across section may reveal a microstructure resembling ripples or wavesthat are indicative of solidified melt pools that may be formed duringthe 3D printing process. The repetitive layered structure of thesolidified melt pools relative to an external plane of the 3D object mayreveal the orientation at which the part was printed, since thedeposition of the melt pools is in a substantially horizontal plane.

In some embodiments, the cross section of the 3D object reveals asubstantially repetitive microstructure (e.g., grain structure). Themicrostructure (e.g., grain structure) may comprise substantiallyrepetitive variations in material composition, grain orientation,material density, degree of compound segregation or of elementsegregation o grain boundaries, material phase, metallurgical phase,crystal phase, crystal structure, material porosity, or any combinationthereof. The microstructure (e.g., grain structure) may comprisesubstantially repetitive solidification of layered inch pools. Thesubstantially repetitive microstructure may have an average height of atleast about 0.5 μm, 1 μm, 5 μm, 7 μm, 20 μm, 30 μm, 40 μm, 50 μm, 60 μm,70 μm, 80 μm, 90 μm, 100 μm, 150 μm, 200 μm, 250 μm, 300 μm, 350 μm, 400μm, 450 μm, 500 μm, or 1000 μm. The substantially repetitivemicrostructure may have an average height of at most about 1000 μm, 500μm, 450 μm, 400 μm, 350 μm, 300 μm, 250 μm, 200 μm, 150 μm, 100 μm, 90μm, 80 μm, 70 μm, 60 μm, 50 μm, 40 μm, 30 μm, 20 μm, or 10 μm. Thesubstantially repetitive microstructure may have an average height ofany value between the afore-mentioned values (e.g., from about 0.5 μm toabout 1000 μm, from about 15 μm, to about 50 μm, from about 5 μm toabout 150 μm, front about 20 μm to about 100 μm, or from about 10 μm toabout 80 μm). The microstructure (e.g., melt pool) height may correspondto the height of a layer of hardened material.

In some embodiments, the 3D object comprises a reduced amount ofconstraints (e.g., supports). The 3D object may comprise lessconstraints. The reduced amount may be relative to prevailing 3Dprinting methodologies in the art (e.g., respective methodologies). The3D object may be less constraint (e.g., relative to prevailing 3Dprinting methodologies in the art). The 3D object may be constraint less(e.g., supportless).

In some embodiments, the pre-transformed material within the materialbed can be configured to provide support to the 3D object. Thepre-transformed material may be a particulate material. The particulatematerial may be flowable (e.g., before, after, and/or during the 3Dprinting). The particulate material in any of the disposed layers in thematerial bed may be flowable (e.g., before, after, and/or during the 3Dprinting). Before, during and/or at the end of the 3D printing process,the material that did not transform may be flowable. The material thatdid not transform to form the 3D object (or a portion thereof) may bereferred to as a “remainder.” In some instances, a low flowabilityparticulate material (e.g., powder) can be capable of supporting a 3Dobject better than a high flowability powder. A low flowabilityparticulate material can be achieved inter alia with a particulatematerial composed of relatively small particles, with particles ofnon-uniform size or with particles that attract each other. Theparticulate material may be of low, medium, or high flowability. Theparticulate material may have compressibility of at least about 1%, 2%,3%, 4%, 5%, 6%, 7%, 8%, 9%, or 10% in response to an applied force of 15kilo Pascals (kPa). The particulate material may have a compressibilityof at most about 9%, 8%, 7%, 6%, 5%, 4.5%, 4.0%, 3.5%, 3.0%, 2.5%, 2.0%,1.5%, 1.0%, or 0.5% in response to an applied force of 15 kilo Pascals(kPa). The particulate material may have basic flow energy of at leastabout 100 milli-Joule (mJ), 200 mJ, 300 mJ, 400 mJ, 450 mJ, 500 mJ, 550mJ, 600 mJ, 650 mJ, 700 mJ, 750 mJ, 800 mJ, or 900 mJ. The particulatematerial may have basic flow energy of at most about 200 mJ, 300 mJ, 400mJ, 450 mJ, 500 mJ, 550 mJ, 600 mJ, 650 mJ, 700 mJ, 750 mJ, 800 mJ, 900mJ, or 1000 mJ. The particulate material may have basic flow energy inbetween the above listed values of basic flow energy values (e.g., fromabout 100 mj to about 1000 mJ, from about 100 mj to about 600 mJ, orfrom about 500 mj to about 1000 mJ). The particulate material may have aspecific energy of at least about 1.0 milli-Joule per gram (mJ/g), 1.5mJ/g, 2.0 mJ/g, 2.5 mJ/g, 3.0 mJ/g, 3.5 mJ/g, 4.0 mJ/g, 4.5 mJ/g, or 5.0mJ/g. The particulate material may have a specific energy of at most5.0mJ/g, 4.5 mJ/g, 4.0 mJ/g, 3.5 mJ/g, 3.0 mJ/g, 2.5 mJ/g, 2.0 mJ/g, 1.5mJ/g, or 1.0 mJ/g. The particulate material may have a specific energyin between any of the above values of specific energy (e.g., from about1.0 mJ/g to about 5.0 mJ/g, from about 3.0 mJ/g to about 5 mJ/g, or fromabout 1.0 mJ/g to about 3.5 mJ/g).

Dining its formation (e.g., layerwise generation), the 3D object canhave one or more auxiliary features. During its formation (e.g.,layerwise generation), the 3D object can be devoid of any auxiliaryfeatures. The auxiliary feature(s) can be supported by the material(e.g., powder) bed and/or by the enclosure. In some instances, theauxiliary supports may connect to the enclosure (e.g., the platform).Connected may comprise anchored. In some instances, the auxiliarysupports may not connect (e.g., be anchored) to the enclosure (e.g., theplatform). For example, the auxiliary supports may contact (e.g., touch)and not connect (e.g., be anchored) to the enclosure (e.g., theplatform). The 3D object comprising one or more auxiliary supports, ordevoid of auxiliary supports may be suspended (e.g., float) in thematerial bed. The floating 3D object (with or without the one or moreauxiliary supports) may contact or not contact the enclosure.

The term “auxiliary features,” as used herein, generally refers tofeatures that are part of a printed 3D object, but are not part of therequested, intended, designed, ordered, modeled, or final 3D object.Auxiliary feature(s) (e.g., auxiliary supports) may provide structuralsupport during and/or subsequent to the formation of the 3D object.Auxiliary features may enable the removal of energy from the 3D objectwhile it is being formed. Examples of auxiliary features comprise theplatform (e.g., building platform and/or base), heat fins, wires,anchors, handles, supports, pillars, columns, frame, footing, scaffold,flange, projection, protrusion, mold (a.k.a. mould), or otherstabilization features. In some instances, the auxiliary support is ascaffold that encloses the 3D object or part thereof. The scaffold maycomprise lightly sintered or lightly fused pre-transformed material. Thescaffold may engulf and/or support at least a portion of a 3D object.The scaffold may reduce the deformation and/or deformability of the atleast a portion of a 3D object. The scaffold may support at least aportion of the 3D object from 1, 2, 3, 4, 5, or 6 spatial directions.The 3D object can have auxiliary features that can be supported by thematerial bed and not touch the base, substrate, container accommodatingthe material bed, and/or the bottom of the enclosure. The 3D part (e.g.,3D object) in a complete or partially formed state can be completelysupported by the material bed (e.g., without being anchored to thesubstrate, base, container accommodating the material bed, orenclosure). The 3D object in a complete or partially formed state can be(completely) supported by the material bed (e.g., without touchinganything except the material bed). The 3D object in a complete orpartially formed state can be suspended in the material bed withoutresting on any additional support structures. In some cases, the 3Dobject in a complete or partially formed (i.e., nascent) state canfreely float (e.g., anchorless) in the material bed. Suspended may befloating, disconnected, anchorless, detached, non-adhered, or free. Insome examples, the 3D object may not be anchored (e.g., connected) to atleast a part of the enclosure (e.g., during formation of the 3D object,and/or during formation of at least one layer of the 3D object). Theenclosure may comprise a platform and/or wall that define the materialbed. The 3D object may not touch and/or not contact enclosure (e.g.,during formation of at least one layer of the 3D object). The 3D objectbe suspended (e.g., float) in the material bed. The scaffold maycomprise a continuously sintered (e.g., lightly sintered) structure thatis at most 1 millimeter (mm), 2 mm, 5 mm or 10 mm. The scaffold maycomprise a continuously sintered structure that is at least 1 millimeter(mm), 2 mm, 5 mm or 10 mm. The scaffold may comprise a continuouslysintered structure having dimensions between any of the afore-mentioneddimensions (e.g., from about 1 mm to about 10 mm, or from about 1 mm toabout 5 mm). In some examples, the 3D object may be printed without asupporting scaffold. The supporting scaffold may engulf at least aportion of the 3D object (e.g., the entire 3D object). For example, asupporting scaffold that floats in the material bed, or that isconnected to at least a portion of the enclosure.

At times, the printed 3D object is printed without the use of auxiliaryfeatures. The printed 3D object may be printed using a reduced number ofauxiliary features, and/or printed using spaced apart auxiliaryfeatures. In some embodiments, the printed 3D object may be devoid of(one or more) auxiliary support features or auxiliary support featuremarks that are indicative of a presence or removal of the auxiliarysupport feature(s). The 3D object may be devoid of one or more auxiliarysupport features and of one or more marks of an auxiliary feature(including a base structure) that was removed (e.g., subsequent to, orcontemporaneous with, the generation of the 3D object). The printed 3Dobject may comprise a single auxiliary and/or a single auxiliary supportmark The single auxiliary feature (e.g., auxiliary support or auxiliarystructure) may be a platform (e.g., a building platform such as a baseor substrate), or a mold. The auxiliary support may be adhered to theplatform or mold. The 3D object may comprise marks belonging to one ormore auxiliary structures. The 3D object may comprise two or more marksbelonging to auxiliary feature(s). The 3D object may be devoid of markspertaining to at least one auxiliary support. The 3D object may bedevoid of one or more auxiliary support. The mark may comprise variationin grain orientation, variation in layering orientation, layeringthickness, material density, the degree of compound segregation to grainboundaries, material porosity, the degree of element segregation tograin boundaries, material phase, metallurgical phase, crystal phase, orcrystal structure; wherein the variation may not have been created bythe geometry of the 3D object alone, and may thus be indicative of aprior existing auxiliary support that was removed. The variation may beforced upon the generated 3D object by the geometry of the support. Insome instances, the 3D structure of the printed object may be forced bythe auxiliary support(s) (e.g., by a mold). For example, a mark may be apoint of discontinuity that is not explained by the geometry of the 3Dobject, which does not include any auxiliary support(s). A mark may be asurface feature that cannot be explained by the geometry of a 3D object,which does not include any auxiliary support(s) (e.g., a mold). The twoor more auxiliary features or auxiliary support feature marks may bespaced apart by a spacing distance of at least 1.5 millimeters (mm), 2mm, 2.5 mm, 3 mm, 3.5 mm, 4 mm, 4.5 mm, 5 mm, 5.5 mm, 6 mm, 6.5 mm, 7mm, 7.5 mm, 8 mm, 8.5 mm, 9 mm, 9.5 mm, 10 mm, 10.5 mm, 11 nun, 11.5 mm,12 mm, 12.5 mm, 13 mm, 13.5 mm, 14 mm, 14.5 mm, 1.5 mm, 15.5 mm, 16 mm,20 mm, 20.5 mm, 21 nun, 25 mm, 30 mm, 30.5 mm, 31 mm, 35 mm, 40 mm, 40.5mm, 41 mm, 45 mm, 50 mm, 80 mm, 100 mm, 200 mm, 300 mm, or 500 mm. Thetwo or more auxiliary support features or auxiliary support featuremarks may be spaced apart by a spacing distance of any value between theafore-mentioned auxiliary support space values (e.g., from 1.5 mm to 500mm, from 2 mm to 100 mm, from 15 mm to 50 mm, or from 45 mm to 200 mm).Collectively referred to herein as the “auxiliary feature spacingdistance.”

At times, the 3D object comprises a layered structure indicative of 3Dprinting process that is devoid of one or more auxiliary supportfeatures or one or more auxiliary support feature marks that areindicative of a presence or removal of the one or more auxiliary supportfeatures. The 3D object may comprise a layered structure indicative of3D printing process, which includes one, two, or more auxiliary supportmarks. The auxiliary support structure may comprise a supportingscaffold. The supporting scaffold may comprise a dense arrangement(e.g., array) of support structures. The support(s) or support mark(s)can stein from or appear on the surface of the 3D object. The auxiliarysupports or support marks can stem from or appear on an external surfaceand/or on an internal surface (e.g., a cavity within the 3D object). Thelayered 3D structure can have a layering plane. In one example, twoauxiliary support features or auxiliary support :feature marks presentin the 3D object may be spaced apart by the auxiliary feature spacingdistance.

At times, a portion of the 3D object is formed at an angle from the oneor more auxiliary supports. FIG. 11, shows an example of a schematiccoordinate system. Line 1104 represents a vertical cross section of alayering plane. Line 1103 represents the straight line connecting thetwo auxiliary supports or auxiliary supports marks. Line 1102 representthe normal to the layering plane. Line 1101 represents the direction ofthe gravitational field. The acute (i.e., sharp) angle alpha between thestraight line connecting the two auxiliary supports or auxiliary supportmarks and the direction of normal to the layering plane may be at leastabout 45 degrees(°), 50°, 55°, 60°, 65°, 70°, 75°, 80°, or 85°. Theacute angle alpha between the straight line connecting the two auxiliarysupports or auxiliary support marks and the direction of normal to thelayering plane may be at most about 90°, 85°, 80°, 75°, 70°, 65°, 60°,55°, 50°, or 45°. The acute angle alpha between the straight lineconnecting the two auxiliary supports or auxiliary support marks and thedirection of normal to the layering plane may be any angle range betweenthe afore-mentioned angles (e.g., from about 45 degrees(°), to about90°, from about 60° to about 90°, from about 75° to about 90°, fromabout 80° to about 90°, or from about 85° to about 90°). The acute anglealpha between the straight line connecting the two auxiliary supports orauxiliary support marks and the direction normal to the layering planemay from about 87° to about 90°. An example of a layering plane can beseen in FIG. 7 showing a vertical cross section of a 3D object 711 thatcomprises layers 1 to 6, each of which are substantially planar In theschematic example in FIG. 7, the layering plane of the layers can be thelayer. For example, layer 1 could correspond to both the layer and thelayering plane of layer 1. When the layer is (e.g., substantially) notplanar (e.g., FIG. 7, layer 5 of 3D object 712), the layering plane cancorrespond to the average plane of the layer. The two auxiliary supportsor auxiliary support feature marks can be on the same surface (e.g.,external surface of the 3D object). The same surface can be an externalsurface or an internal surface (e.g., a surface of a cavity within the3D object). When the angle between the shortest straight line connectingthe two auxiliary supports or auxiliary support marks and the directionof normal to the layering plane is greater than 90 degrees, one canconsider the complementary acute angle. In some embodiments, any twoauxiliary supports or auxiliary support marks are spaced apart by atleast about 10.5 millimeters or more. In some embodiments, any twoauxiliary supports or auxiliary support marks are spaced apart by atleast about 40.5 millimeters or more. In some embodiments, any twoauxiliary supports or auxiliary support marks are spaced apart by theauxiliary feature spacing distance.

At times, the 3D object is formed without one or more auxiliary featuresand/or without contacting a platform (e.g., a base, a substrate, or abottom of an enclosure). The one or more auxiliary features (which mayinclude a base support) can be used to hold or restrain the 3D objectduring formation. In some cases, auxiliary features can be used toanchor and/or hold a 3D object or a portion of a 3D object in a materialbed (e.g., with or without contacting the enclosure, or with or withoutconnecting to the enclosure). The one or more auxiliary features can bespecific to a 3D object and can increase the time, energy, materialand/or cost required to form the 3D object. The one or more auxiliaryfeatures can be removed prior to use or distribution of the 3D object.The longest dimension of a cross-section of an auxiliary feature can beat most about 50 nm, 100 nm, 200 nm, 300 nm, 400 nm, 500 nm, 600 nm, 700nm, 800 nm, 900 nm, or 1000 nm, 1 μm, 3 μm, 10 μm, 20 μm, 30 μm, 100 μm,200 μm, 300 μm, 400 μm, 500 μm, 700 μm, 1 mm, 3 mm, 5 mm, 10 mm, 20 mm,30 mm, 50 mm, 100 mm, or 300 mm. The longest dimension (e.g., FLS) of across-section of an auxiliary feature can be at least about 50 nm, 100nm, 200 nm, 300 nm, 400 nm, 500 nm, 600 nm, 700 nm, 800 nm, 900 nm, or1000 nm, 1 μm, 3 μm, 10 μm, 20 μm, 30 μm, 100 μm, 200 μm, 300 μm, 400μm, 500 μm, 700 μm, 1 mm, 3 mm, 5 mm, 10 mm, 20 mm, 30 mm, 50 mm, 100mm, or 300 mm. The longest dimension of a cross-section of an auxiliaryfeature can be any value between the above-mentioned values (e.g., fromabout 50 mm to about 300 mm, from about 5 μm to about 10 mm, from about50 nm to about 10 mm, or from about 5 mm to about 300 mm). Eliminatingthe need for auxiliary features can decrease the time, energy, material,and/or cost associated with generating the 3D object (e.g., 3D part). Insome examples, the 3D object may be formed with auxiliary features. Insome examples, the 3D object may be formed while connecting to thecontainer accommodating the material bed (e.g., side(s) and/or bottom ofthe container).

In some examples, the diminished number of auxiliary supports or lack ofone or more auxiliary supports, will provide a 3D printing process thatrequires a smaller amount of material, energy, material, and/or cost ascompared to commercially available 3D printing processes. In someexamples, the diminished number of auxiliary supports or lack of one ormore auxiliary supports, will provide a 3D printing process thatproduces a smaller amount of material waste as compared to commerciallyavailable 3D printing processes. The smaller amount can be smaller by atleast about 1.1, 1.3, 1.5, 2, 3, 4, 5, 6, 7, 8, 9, or 10. The smalleramount may be smaller by any value between the aforesaid values (e.g.,from about 1.1 to about 10, or from about 1.5 to about 5).

In some examples, at least a portion of the 3D object can be verticallydisplaced (e.g., sink) in the material bed. At least a portion of the 3Dobject can be surrounded by pre-transformed material within the materialbed (e.g., submerged). At least a portion of the 3D object can rest inthe pre-transformed material without substantial vertical movement(e.g., displacement). Lack of substantial vertical displacement canamount to a vertical movement (e.g., sinking) of at most about 40%, 20%,10%, 5%, or 1% of the layer thickness. Lack of substantial sinking canamount to at most about 100 μm, 30 μm, 10 μm, 3 μm, or 1 μm. At least aportion of the 3D object can rest in the pre-transformed materialwithout substantial movement (e.g., horizontal, vertical, and/orangular). Lack of substantial movement can amount to a movement of atmost 100 μm, 30 μm, 10 μm, 3 μm, or 1 μm. The 3D object can rest on thesubstrate when the 3D object is vertically displaced (e.g., sunk) orsubmerged in the material bed.

FIG. 1 depicts an example of a system that can be used to generate a 3Dobject using a 3D printing process disclosed herein. The system caninclude an enclosure (e.g., a chamber 107). At least a fraction of thecomponents in the system can be enclosed in the chamber At least afraction of the chamber can be filled with a gas to create a gaseousenvironment (i.e., an atmosphere). The gas can be an inert gas (e.g.,Argon, Neon, Helium, Nitrogen). The chamber can be filled with anothergas or mixture of gases. The gas can be a non-reactive gas (e.g., aninert gas). The gaseous environment can comprise argon, nitrogen,helium, neon, krypton, xenon, hydrogen, carbon monoxide, or carbondioxide. The pressure in the chamber can be at least 10⁻⁷ Torr, 10⁻⁶Torr, 10⁻⁵ Torr, 10⁻⁴ Torr, 10⁻³ Torr, 10⁻² Torr, 10⁻¹ Torr, 1 Torr, 10Torr, 100 Torr, 1 bar, 2 bar, 3 bar, 4 bar, 5 bar, 10 bar, 20 bar, 30bar, 40 bar, 50 bar, 100 bar, 200 bar, 300 bar, 400 bar, 500 bar, or1000 bar. The pressure in the chamber can be at least about 100 Torr,200 Torr, 300 Torr, 400 Torr, 500 Torr, 600 Torr, 700 Torr, 720 Torr,740 Torr, 750 Torr, 760 Torr, 900 Torr, 1000 Torr, 1100 Torr, or 1200Torr. The pressure in the chamber can be at most about 10⁻⁷ Torr, 10⁻⁶Torr, 10⁻⁵ Torr, or 10⁻⁴ Torr, 10⁻³ Torr, 10⁻² Torr, 10⁻¹ Torr, 1 Torr,10 Torr, 100 Torr, 200 Torr, 300 Torr, 400 Ton, 500 Torr, 600 Torr, 700Torr, 720 Torr, 740 Torr, 750 Torr, 760 Torr, 900 Torr, 1000 Torr, 1100Torr, or 1200 Torr. The pressure in the chamber can he at a rangebetween any of the afore-mentioned pressure values (e.g., from about10⁻⁷ Torr to about 1200 Torr, from about 10⁻⁷ Torr to about 1 Torr, fromabout 1 Torr to about 1200 Torr, or from about 10⁻² Torr to about 10Torr). The pressure can be measured by a pressure gauge. The pressurecan be measured at ambient temperature (e.g., RT.), cryogenictemperature, or at the temperature of the inciting point of thepre-transformed material. In some cases, the pressure in the chamber canbe standard atmospheric pressure. In some cases, the pressure in thechamber can be ambient pressure (i.e., neutral pressure). In someexamples, the chamber can be under vacuum pressure. In some examples,the chamber can be under a positive pressure (i.e., above ambientpressure).

At times, the chamber comprises two or more gaseous layers. The gaseouslayers can be separated by molecular weight or density such that a firstgas with a first molecular weight or density is located in a firstregion, and a second gas with a second molecular weight or density islocated in a second region of the chamber above or below the firstregion. The first molecular weight or density may be smaller than thesecond molecular weight or density. The first molecular weight ordensity may be larger than the second molecular weight or density. Thegaseous layers can be separated by a temperature difference. The firstgas can be in a lower region of the chamber relative to the second gas.The second gas and the first gas can be in adjacent locations. Thesecond gas can be on top of, over, and/or above the first gas. In somecases, the first gas can be argon and the second gas can be helium. Themolecular weight or density of the first gas can be at least about 1.5*,2*, 3*, 4*, 5*, 10*, 15*, 20*, 25*, 30*, 35*, 40*, 50*, 55*, 60*, 70*,75*, 80*, 90*, 100*, 200*, 300*, 400*, or 500* larger or greater thanthe molecular weight or density of the second gas (e.g., measured atambient temperature). The molecular weight of the first gas can behigher than the molecular weight of air. The molecular weight or densityof the first gas can be higher than the molecular weight or density ofoxygen gas (e.g., O₂). The molecular weight or density of the first gascan be higher than the molecular weight or density of nitrogen gas(e.g., N₂). The molecular weight or density of the first gas may belower than that of oxygen gas and/or nitrogen gas.

At times, the first gas with the relatively higher molecular weight ordensity fills a region of the system where at least a fraction of thepre-transformed material is stored. The first gas with the relativelyhigher molecular weight or density can fill a region of the systemand/or apparatus where the 3D object is formed. Alternatively, thesecond gas with the relatively lower molecular weight or density canfill a region of the system and/or apparatus where the 3D object isformed. The material layer can be supported on a platform. The platformmay comprise a substrate (e.g., 109). The substrate can have a circular,rectangular, square, or irregularly shaped cross-section. The platformmay comprise a base disposed above the substrate. The platform maycomprise a base (e.g., 102) disposed between the substrate and amaterial layer (or a space to be occupied by a material layer). Athermal control unit (e.g., a cooling member such as a heat sink or acooling plate, or a heating plate 113) can be provided inside of theregion where the 3D object is formed or adjacent to (e.g., above) timeregion where the 3D object is formed. The thermal control unit maycomprise a thermostat. Additionally, or alternatively, the thermalcontrol unit can be provided outside of the region where the 3D objectis formed (e.g., at a predetermined distance). In some cases, thethermal control unit can form at least one section of a boundary regionwhere the 3D object is formed (e.g., the container accommodating thematerial bed).

At times, the concentration of oxygen and/or humidity in the enclosure(e.g., chamber) can be minimized (e.g., below a predetermined thresholdvalue). The gas composition of the chanter may contain a level of oxygenand/or humidity that is at most about 100 parts per billion (ppb). 10ppb, 1 ppb, 0.1 ppb, 0.01 ppb, 0.001 ppb, 100 parts per million (ppm),10 ppm, 1 ppm, 0.1 ppm, 0.01 ppm, or 0.001 ppm. The gas composition ofthe chanter can contain an oxygen and/or humidity level between any ofthe aforementioned values (e.g., from about 100 ppb to about 0.001 ppm,from about 1ppb to about 0.01 ppm, or from about 1 ppm to about 0.1ppm). The gas composition may be measures by one or more sensors (e.g.,an oxygen and/or humidity sensor). The chamber can be opened at thecompletion of a formation of a 3D object. When the chamber is opened,ambient air containing oxygen and/or humidity can enter the chanter.Exposure of one or more components inside the chamber to air can bereduced by, for example, flowing an inert gas while the chamber is open(e.g., to prevent catty of ambient air), or by flowing a heavy gas(e.g., argon) that tests on the surface of the material bed. In somecases, components that absorb oxygen and/or humidity onto theirsurface(s) can be sealed while the enclosure (e.g., chamber) is open(e.g., to the ambient environment).

At times, the chamber is configured such that gas inside of the chamberhas a relatively low leak rate from the chamber to an environmentoutside of the chamber. In some cases, the leak rate call be at mostabout 100 milliTorr/minute (mTorr/min), 50 mTorr/min, 2.5 mTorr/min, 15mTorr/min, 10 mTorr/min, 5 mTorr/min, 1 mTorr/min, 0.5 mTorr/min, 0.1mTorr/min, 0.05 mTorr/min, 0.01 mTorr/min, 0.005 mTorr/min, 0.001mTorr/min, 0.0005 mTorr/min, or 0.0001 mTorr/min. The leak rate may bebetween any of the aforementioned leak rates (e,g, from about 0.0001mTorr/min to about, 100 mTorr/min, from about 1 mTorr/min to about, 100mTorr/min, or from about 1 mTorr/min to about, 100 mTorr/min). The leakrate may be measured by one or more pressure gauges and/or sensors(e.g., at ambient temperature). The enclosure can be sealed such thatthe leak rate of gas from inside the chamber to an environment outsideof the chamber is low (e.g., below a certain level). The seals cancomprise O-rings, rubber seals, metal seals, load-locks, or bellows on apiston. In some cases, the chamber can have a controller configured todetect leaks above a specified leak rate (e.g., by using at least onesensor). The sensor may be coupled to a controller. In some instances,the controller is able to identify and/or control (e.g., direct and/orregulate). For example, the controller may be able to identify a leak bydetecting a decrease in pressure in side of the chamber over a giventime interval.

One or more of the system components can be contained in the enclosure(e.g., chamber). The enclosure can include a reaction space that issuitable for introducing precursor to form a 3D object, such aspre-transformed (e.g., powder) material. The enclosure can contain theplatform. In some cases, the enclosure can be a vacuum chamber, apositive pressure chamber, or an ambient pressure chamber. The enclosurecan comprise a gaseous environment with a controlled pressure,temperature, and/or gas composition. The gas composition in theenvironment contained by the enclosure can comprise a substantiallyoxygen free environment. For example, the gas composition can contain atmost about 100,000 parts per million (ppm), 10,000 ppm, 1000 ppm, 500ppm, 400 ppm, 200 ppm, 100 ppm, 50 ppm, 10 ppm, 5 ppm, 1 ppm, 100,000parts per billion (ppb), 10,000 ppb, 1000 ppb, 500 ppb, 400 ppb, 200ppb, 100 ppb, 50 ppb, 10 ppb, 5 ppb, 1 ppb, 100,000 parts per trillion(ppt). 10.000 ppt. 1000 ppt, 500 ppt, 400 ppt, 200 ppt, 100 ppt, 50 ppt,10 ppt, 5 ppt, or 1 ppt oxygen. The gas composition in the environmentcontained within the enclosure can comprise a substantially moisture(e.g., water) free environment. The gaseous environment can comprise atmost about 100,000 ppm, 10,000 ppm, 1000 ppm, 500 ppm, 400 ppm, 200 ppm,100 ppm, 50 ppm, 10 ppm, 5 ppm, 1 ppm, 100,000 ppb. 10,000 ppb, 1000ppb, 500 ppb, 400 ppb, 200 ppb, 100 ppb, 50 ppb, 10 ppb, 5 ppb, 1 ppb,100,000 ppt, 10,000 ppt, 1000 ppt, 500 ppt, 400 ppt, 200 ppt, 100 ppt,50 ppt, 10 ppt, 5 ppt, or 1 ppt water. The gaseous environment cancomprise a gas selected from the group consisting of argon, nitrogen,helium, neon, krypton, xenon, hydrogen, carbon monoxide, carbon dioxide,and oxygen. The gaseous environment can comprise air. The chamberpressure can be at least about 10⁻⁷ Torr, 10⁻⁶ Torr, 10⁻⁵ Torr, 10⁻⁴Torr, 10⁻³ Torr, 10⁻² Torr, 10⁻¹ Torr, 1 Torr, 10 Torr, 100 Torr, 1 bar,760 Torr, 1000 Torr, 1100 Torr, 2 bar, 3 bar, 4 bar, 5 bar, or 10 bar.The chamber pressure can be of any value between the afore-mentionedchanter pressure values (e.g., from about 10 ⁻⁷ Torr to about 10 bar,from about 10⁻⁷ Torr to about 1 bar, or from about 1 bar to about 10bar). In some cases, the enclosure pressure can be standard atmosphericpressure. The gas can be an ultrahigh purity gas. The ultrahigh puritygas can be at least about 99%, 99.9%, 99.99%, or 99.999% pure. The gasmay comprise less than about 2 ppm oxygen, less than about 3 ppmmoisture, less than about 1 ppm hydrocathons, or less than about 6 ppmnitrogen.

The enclosure can be maintained under vacuum or under an inert, dry,non-reactive and/or oxygen reduced (or otherwise controlled) atmosphere(e.g., a nitrogen (N ₂), helium (He), or argon (Ar) atmosphere). In someexamples, the enclosure is under vacuum. In some examples, the enclosureis under pressure of at most about 1 Torr, 10⁻³ Torr, 10⁻⁶ Torr, or 10⁻⁸Torr. The atmosphere can be furnished by providing an inert, dry,non-reactive, and/or oxygen reduced gas (e.g., Ar). The atmosphere canbe furnished by flowing the gas through the enclosure (e.g., chamber).

The system and/or apparatus components described herein can be adaptedand configured to generate a 3D object. The 3D object can be generatedthrough a 3D printing process. The 3D printing process may be any 3Dprinting process described herein. A first layer of pre-transformedmaterial can be provided adjacent to a platform. A platform (e.g., base)can be a previously formed layer of the 3D object or any other surfaceupon which a layer or bed of pre-transformed material is spread, held,placed, adhered, attached, or supported. When the first layer of the 3Dobject is generated, the first material layer can be formed in thematerial bed without a platform (e.g., base), without one or moreauxiliary support features (e.g., rods), or without other supportingstructure other than the pre-transformed material (e.g., within thematerial bed). Subsequent layers can be formed such that at least oneportion of the subsequent layer fused (e.g., melts or sinters) fuses,binds and/or otherwise connects to the at least a portion of apreviously formed layer (or portion thereof). The at least a portion ofthe previously formed layer that can be transformed and optionallysubsequently harden into a hardened material. The at least a portion ofthe previously formed layer that can acts as a platform (e.g., base) forformation of the 3D object. In some cases, the first layer comprises atleast a portion of the platform (e.g., base). The pre-transformedmaterial layer can comprise particles of homogeneous or heterogeneoussize and/or shape.

FIG. 12 shows an example of an optical setup in which an energy beam isprojected from the energy source 1206, and is deflected by two mirrors1205, and travels through an optical element 1204 prior to reachingtarget 1202 (e.g., an exposed surface of a material bed comprising apre-transformed material and/or hardened or partially hardened materialsuch as from a previous transformation operation). The optical element1204 can be an optical window, in which case the incoming beam 1207 issubstantially unaltered after crossing the optical element 1204. Theoptical element 1204 can be a focus altering device, in which case thefocus (e.g., cross-section) of the incoming beam 1207 is altered afterpassing through the optical element 1204 and emerging as the beam 1203.The controller may control the scanner (e.g., the mirrors) that directsthe movement of the transforming energy beam and/or platform (e.g., inreal time).

The system and/or apparatus described herein comprises at least oneenergy source (e.g., the transforming energy source generating thetransforming energy beam). The energy source may be used to transform atleast a portion of the material bed into a transformed material(designated herein also as “transforming energy source”). Thetransforming energy source may project an energy beam (herein also“transforming energy beam”). The transforming energy beam may be anyenergy beam (e.g., type-1 energy beam or type-2 energy beam) and theassociated processes disclosed in U.S. provisional patent applicationNo. 62/265,817, filed on Dec. 10, 2015, titled “APPARATUSES, SYSTEMS ANDMETHODS FOR EFFICIENT THREE DIMENSIONAL PRINTING,” PCT patentapplication number PCT/US/2016/066000, filed on Dec. 9, 2016, titled“SKILLFUL THREE-DIMENSIONAL PRINTING,” and U.S. patent application Ser.No. 15/374,318, filed on Dec. 9, 2016, “SKILLFUL THREE-DIMENSIONALPRINTING,” each of which is incorporated herein by reference in itsentirety where non-contradictory. The transforming energy source may beany energy source disclosed in U.S. provisional patent application No.62/265,817, PCT patent application number PCT/US2016/066000, and U.S.patent application Ser. No. 15/374,318, each of which is incorporatedherein by reference in its entirety where non-contradictory. The energybeam may travel (e.g., scan) along a path. The path may be predetermined(e.g., by the controller). The methods, systems and/or apparatuses maycomprise at least a second energy source. The second energy source maygenerate a second energy (e.g., second energy beam). The first and/orsecond energy may transform at least a portion of the pre-transformedmaterial in the material bed to a transformed material. In someembodiments, the first and/or second energy source may heat but nottransform at least a portion of the pre-transformed material in thematerial bed. In some cases, the system can comprise 1, 2, 3, 4, 5, 6,7, 8, 9, 10, 30, 100, 300, 1000 or more energy beams and/or sources. Thesystem can comprise an array of energy sources (e.g., laser diodearray). Alternatively, or additionally the surface, material bed, 3Dobject (or part thereof), or any combination thereof may be heated by aheating mechanism The heating mechanism may comprise dispersed energybeams. In some cases, the at least one energy source is a single (e.g.,first) energy source.

At times, an energy source is a source configured to deliver energy toan area (e.g., a confined area). An energy source can deliver energy tothe confined area through radiative heat transfer. The energy source canproject energy (e.g., heat energy, and/or energy beam). The energy(e.g., beam) can interact with at least a portion of the material in thematerial bed. The energy can heat the material in the material bedbefore, during and/or after the pre-transformed material is beingtransformed (e.g., melted). The energy can heat at least a fraction of a3D object at any point during formation of the 3D object. Alternatively,or additionally, the material bed may be heated by a heating mechanismprojecting energy (e.g., radiative heat and/or energy beam). The energymay include an energy beam and/or dispersed energy (e.g., radiator orlamp). The energy may include radiative heat. The radiative heat may beprojected by a dispersive energy source (e.g., a heating mechanism)comprising a lamp, a strip heater (e.g., mica strip heater, or anycombination thereof), a heating rod (e.g., quartz rod), or a radiator(e.g., a panel radiator). The heating mechanism may comprise aninductance heater. The heating mechanism may comprise a resistor (e.g.,variable resistor). The resistor may comprise a varistor or rheostat. Amultiplicity of resistors may be configured in series, parallel, or anycombination thereof. In some cases, the system can have a single (e.g.,first) energy source that is used to transform at least a portion of thematerial bed. An energy source can be a source configured to deliverenergy to an area (e.g., a confined area). An energy source can deliverenergy to the confined area through radiative heat transfer (e.g., asdescribed herein).

At times, the energy beam includes a radiation comprising anelectromagnetic, or charged particle beam. The energy beam may includeradiation comprising electromagnetic, electron, positron, proton,plasma, radical or ionic radiation. The electromagnetic beam maycomprise microwave, infrared, ultraviolet, or visible radiation. Theenergy beam may include an electromagnetic energy beam, electron beam,particle beam, or ion beam. An ion beam may include a cation or ananion. A particle beam may include radicals. The electromagnetic beammay comprise a laser beam. The energy beam may comprise plasma. Theenergy source may include a laser source. The energy source may includean electron gun. The energy source may include an energy source capableof delivering energy to a point or to an area. In some embodiments, theenergy source can be a laser source. The laser source may comprise aCO₂, Nd:YAG, Neodymium (e.g., neodymium-glass), an Ytterbium, or anexcimer laser. The energy source may include an energy source capable ofdelivering energy to a point or to an area. The energy source (e.g.,transforming energy source) can provide an energy beam having an energydensity of at least about 50 joules/cm² (J/cm²), 100 J/cm², 200 J/cm²,300 J/cm², 400 J/cm², 500 J/cm², 600 J/cm², 700 J/cm², 800 J/cm², 1000J/cm², 1500 J/cm², 2000 J/cm², 2500 J/cm², 3000 J/cm², 3500 J/cm², 4000J/cm², 4500 J/cm², or 5000 J/cm². The energy source can provide anenergy beam having an energy density of at most about 50 J/cm², 100J/cm², 200 J/cm², 300 J/cm², 400 J/cm², 500 J/cm², 600 J/cm², 700 J/cm²,800 J/cm², 1000 J/cm², 500 J/cm², 1000 J/cm², 1500 J/cm², 2000 J/cm²,2500 J/cm², 3000 J/cm², 3500 J/cm², 4000 J/cm², 4500 J/cm², or 5000J/cm². The energy source can provide an energy beam having an energydensity of a value between the afore-mentioned values (e.g., from about50 J/cm²to about 5000 J/cm² , from about 200 J/cm² to about 1500 J/cm²,from about 1500 J/cm² to about 2500 J/cm², from about 100 J/cm² to about3000 J/cm², or from about 2500 J/cm²to about 5000 J/cm²). In an example,a laser can provide light energy at a peak wavelength of at least about100 nanometer (nm), 500 nm, 750 nm, 1000 nm, 1010 nm, 1020 nm, 1030 nm,1040 nm, 1050 nm, 1060 nm, 1070 nm, 1080 nm, 1090 nm, 1100 nm, 1200 nm,1500 nm, 1600 nm, 1700 nm, 1800 nm, 1900 nm, or 2000 nm. In an example alaser can provide light energy at a peak wavelength of at most about2000 nm, 1900 nm, 1800 nm, 1700 nm, 1600 nm, 1500 nm, 1200 nm, 1100 nm,1090 nm, 1080 nm, 1070 nm, 1060 nm, 1050 nm, 1040 nm, 1030 nm, 1020 nm,1010 nm, 1000 nm, 750 nm, 500 nm, or 100 nm. The laser can provide lightenergy at a peak wavelength between any of the afore-mentioned peakwavelength values (e.g., from about 100 nm to about 2000 nm, from about500 nm to about 1500 nm, or from about 1000 nm to about 1100 nm). Theenergy beam (e.g., laser) may have a power of at least about 0.5 Watt(W), 1 W, 2 W, 3 W, 4 W, 5 W, 10 W, 20 W, 30 W, 40 W, 50 W, 60 W, 70 W,80 W, 90 W, 100 W, 120 W, 150 W, 200 W, 250 W, 300 W, 350 W, 400 W, 500W, 750 W, 800 W, 900W, 1000 W, 1500 W, 2000 W, 3000 W, or 4000 W. Theenergy beam may have a power of at most about 0.5 W, 1 W, 2 W, 3 W, 4 W,5 W, 10 W, 20 W, 30 W, 40 W, 50 W, 60 W, 70 W, 80 W, 90 W, 100 W, 120 W,150 W, 200 W, 250 W, 300 W, 350 W, 400 W, 500 W, 750 W, 800 W, 900 W,1000 W, 1500, 2000 W, 3000 W, or 4000 W. The energy beam may have apower between any of the afore-mentioned laser power Values e.g., fromabout 0.5 W to about 100 W, from about 1 W to about 110 W, from about100 W to about 1000 W, or from about 1000 W to about 4000 W). The firstenergy source (e.g., producing the transforming energy beam) may have atleast one of the characteristics of the second energy source.

At times, an energy beam from the energy source(s) is incident on, or isdirected perpendicular to, the surface (also herein “target surface”).The target surface may be an exposed surface of the material bed or anexposed surface of a hardened material. The hardened material may be a3D object or a portion thereof. An energy beam from the energy source(s)can be directed at an acute angle within a value ranging from beingparallel to being perpendicular with respect to the average or meanplane of the target surface. The energy beam can be directed onto aspecified area of at least a portion of the target surface for aspecified time period (e.g., dwell time). The material in target surface(e.g., pre-transformed material such as in a top surface of a materialbed) may absorb the energy from the energy beam and, and as a result, alocalized region of at least the material at the surface, can increasein temperature. The energy beam can be moveable such that it cantranslate (e.g., horizontally, vertically, and/or in an angle). Theenergy source may be movable such that it can translate relative to thetarget surface. The energy beam(s) can be moved via a scanner (e.g., asdisclosed herein). At least two (e.g., all) of the energy sources can bemovable with the same scanner. A least two (e.g., all) of the energybeams can be movable with the same scanner. At least two of the energysource(s) and/or beam(s) can be translated independently of each other.In some cases, at least two of the energy source(s) and//or beam(s) canbe translated at different rates (e.g., velocities). In some cases, atleast two of the energy source(s) and/or beam(s) can be comprise atleast one different characteristic. The characteristics may comprisewavelength, charge, power, amplitude, trajectory, footprint,cross-section, focus, intensity, energy, path, or hatching. The chargecan be electrical and/or magnetic charge.

In some embodiments, the energy source is an array, or a matrix, ofenergy sources e.g., laser diodes). Each of the energy sources in thearray, or matrix, can be independently controlled (e.g., by a controlmechanism) such that the energy beams can be turned off and onindependently. At least a part of the energy sources (e.g., in the arrayor matrix) can be collectively controlled such that the at least two(e.g., all) of the energy sources can be turned off and onsimultaneously. The energy per unit area or intensity of at least twoenergy sources in the matrix or array can be modulated independently(e.g., by a controller). At times, the energy per unit area or intensityof at least two (e.g., all) of the energy sources (e.g., in the matrixor array) can be modulated collectively (e.g., by a controller). Theenergy source can scan along the target surface by mechanical movementof the energy source(s), one or more adjustable reflective mirrors oneor more polygon light scanners, or any combination or permutationthereof. The energy source(s) can project energy using a DLP modulator,a one-dimensional scanner, a two-dimensional scanner, or any combinationthereof. The energy source(s) can be stationary. The material bed (e.g.,target surface) may translate vertically, horizontally, or in an angle(e.g., planar or compound). The translation may be effectuated using ascanner.

At times, the energy source is modulated. The energy beam emitted by theenergy source can be modulated. The modulator can include amplitudemodulator, phase modulator, or polarization modulator. The modulationmay alter the intensity of the energy beam. The modulation may alter thecurrent supplied to the energy source (e.g., direct (modulation). Themodulation may affect the energy beam (e.g., external modulation such asexternal light modulator). The modulation may include direct modulation(e.g., by a modulator). The modulation may include an externalmodulator. The modulator can include an acusto-optic modulator or anelectro-optic modulator. The modulator can comprise an absorptivemodulator or a refractive modulator. The modulation may alter theabsorption coefficient the material that is used to modulate the energybeam. The modulator may alter the refractive index of the material thatis used to modulate the energy beam. The focus of the energy beam may becontrolled (e.g., modulated). At times, the energy beam may be focused.At times, the energy beam may be defocused (e.g., blurred).

At times, the energy source and/or beam is moveable such that it cantranslate relative to the material bed and/or target surface. In someinstances, the energy beam may be movable such that it can translateacross (e.g., laterally) the exposed (e.g., top) surface of the materialbed. The energy beam(s) and/or source(s) can be moved via a scanner. Thescanner may comprise a galvanometer scanner, a polygon, a mechanicalstage (e.g., X-Y stage), a piezoelectric device, gimble, or anycombination of thereof. The galvanometer may comprise a mirror. Thescanner may comprise a modulator. The scanner may comprise a polygonalmirror. The scanner can be the same scanner for two or more energysources and/or beams. The scanner may comprise an optical setup. Atleast two (e.g., each) energy source and/or beam may have a separatescanner. The energy sources can be translated independently of eachother. In some cases, at least two energy sources and/or beams can betranslated at different rates, and/or along different paths. Forexample, the movement of the first energy source may be faster (e.g.,greater rate) as compared to the movement of the second energy source.The systems and/or apparatuses disclosed herein may comprise one or moreshutters (e.g., safety shutters). The energy beam(s), energy source(s),and/or the platform can be moved by the scanner. The galvanometerscanner may comprise a two-axis galvanometer scanner. The scanner maycomprise a modulator (e.g., as described herein). The energy source(s)can project energy using a DLP modulator, a one-dimensional scanner, atwo-dimensional scanner, or any combination thereof. The energysource(s) can be stationary or translatable. The energy source(s) cantranslate vertically, horizontally, or in an angle (e.g., planar orcompound angle). The energy source(s) can be modulated. The scanner canbe included in an optical system (e.g., optical setup) that isconfigured to direct energy from the energy source to a predeterminedposition on the target surface (e.g., exposed surface of the materialbed). The controller can be programmed to control a trajectory of theenergy source(s) with the aid of the optical system. The controller canregulate a supply of energy from the energy source to the material(e.g., at the target surface) to form a transformed material.

At times, the energy beam(s) emitted by the energy source(s) ismodulated. The modulator can include an amplitude modulator, phasemodulator, or polarization modulator. The modulation may alter theintensity of the energy beam. The modulation may alter the currentsupplied to the energy source (e.g., direct modulation). The modulationmay affect the energy beam (e.g., external modulation such as externallight modulator). The modulation may include direct modulation (e.g., bya modulator). The modulation may include an external modulator. Themodulator can include an acusto-optic modulator or an electro-opticmodulator. The modulator can comprise an absorptive modulator or arefractive modulator. The modulation may alter the absorptioncoefficient the material that is used to modulate the energy beam. Themodulator may alter the refractive index of the material that is used tomodulate the energy beam.

At times, the energy beam (e.g., transforming energy beam) comprises aGaussian energy beam. The energy beam may have any cross-sectional shapecomprising an ellipse (e.g., circle), or a polygon. The energy beam mayhave a cross section with a FLS (e.g., diameter) of at least about 30micrometers (μm), 50 μm, 70 μm, 100 μm, 150 μm, 200 μm, 250 μm, or 300μm. The energy beam may have a cross section with a FLS of at most about50 μm, 60 μm, 70 μm, 100 μm, 150 μm, 200 μm, 250 μm, or 300 μm. Theenergy beam may have a cross section with a FLS of any value between theafore-mentioned values (e.g., from about 30 μm to about 300 μm, fromabout 50 μm to about 150 μm, or from about 150 μm to about 300 μm). Attimes, the FLS of a cross section of the energy beam may be extended.The FLS of a cross section of the energy beam may be at least about 0.3millimeter (mm), 0.5 mm, 0.8 mm, 1 mm, 1.5 mm, 2 mm, 2.5 mm, 3 mm, 3.5mm, 4 mm, 4.5 mm, or 5 mm. The FLS of a cross section of the energy beammay be at most about 0.5 mm, 0.8 mm, 1 mm, 1.5 mm, 2 mm, 2.5 mm, 3 mm,3.5 mm, 4 mm, 4.5 mm, or 5 mm. The FLS of a cross section of the energybeam may be between any of the aforementioned values (e.g., from about0.3 mm to about 5 mm, from about 0.3 mm to about 2.5 mm, or from about2.5 mm to about 5 mm).

The powder density (e.g., power per unit area at the target surface) ofthe energy beam may at least about 10000 W/mm², 20000 W/mm², 30000W/mm², 50000 W/mm², 60000 W/mm², 70000 W/mm², 80000 W/mm², 90000 W/mm²,or 100000 W/mm². The powder density of the energy beam may be at mostabout 10000 W/mm², 20000 W/mm², 30000 W/mm², 50000 W/mm², 60000 W/mm²,70000 W/mm², 80000 W/mm², 90000 W/mm², or 100000 W/mm². The powderdensity of the energy beam may be any value between the aforementionedvalues (e.g., from about 10000 W/mm², to about 100000 W/mm², from about10000 W/mm² to about 50000 W/mm², or from about 50000 W/mm² to about100000 W/mm²). The scanning speed of the energy beam may be at leastabout 50 millimeters per second (mm/sec), 100 mm/sec, 500 mm/sec, 1000mm/sec, 2000 mm/sec, 3000 mm/sec, 4000 mm/sec, or 50000 mm/sec. Thescanning speed of the energy beam may be at most about 50 mm/sec, 100mm/sec, 500 mm/sec, 1000 mm/sec, 2000 mm/sec, 3000 mm/sec, 4000 mm/see,or 50000 mm/sec. The scanning speed of the energy beam may any valuebetween the aforementioned values (e.g., from about 50 mm/sec to about50000 mm/sec, from about 50 mm/sec to about 3000 mm/sec, or from about2000 mm/sec to about 50000 mm/sec). The energy beam may be continuous ornon-continuous (e.g., pulsing). The energy beam may be modulated beforeand/or during the formation of a transformed material as part of the 3Dobject. The energy beam may be modulated before and/or during the 3Dprinting process.

In some embodiments, the 3D printing system and/or apparatus is the onedescribed in U.S. provisional patent application No. 62/265,817, PCTpatent application number PCT/US2016/066000, or U.S. patent applicationSer. No. 15/374,318, each of which is incorporated herein by referencein its entirety Where non-contradictory. The 3D printing system orapparatus may comprise a layer dispensing mechanism may dispense thepre-transformed material (e.g., in the direction of the platform),level, distribute, spread, and/or remove the pre-transformed material inthe material bed. The layer dispensing mechanism may be utilized to formthe material bed. The layer dispensing mechanism may be utilized to formthe layer of pre-transformed material (or a portion thereof). The layerdispensing mechanism may be utilized to level (e.g., planarize) thelayer of pre-transformed material (or a portion thereof). The levelingmay be to a predetermined height. The layer dispensing mechanism maycomprise at least one, two or three of a (i) powder dispensing mechanism(e.g., FIG. 1, 116), (ii) powder leveling mechanism (e.g., FIG. 1, 117),and (iii) powder removal mechanism (e.g., FIG. 1, 118). The layerdispensing mechanism may be controlled by the controller (e.g., in realtime). The layer dispensing mechanism or any of its components can beany of those disclosed in U.S. provisional patent application No.62/265,817; PCT patent application number PCT/US2016/066000; U.S. patentapplication Ser. No. 15/374,318; or PCT patent application numberPCT/US15/36802, filed on Jun. 19, 2015, titled “APPARATUSES, SYSTEMS ANDMETHODS FOR THREE-DIMENSIONAL PRINTING,” each of which is incorporatedherein by reference in its entirety where non-contradictory. The layerdispensing system may comprise a hopper. The layer dispensing system maycomprise (e.g., may be) a recoater.

In some embodiments, one or more sensors (at least one sensor) detectthe topology of the exposed surface of the material bed and/or theexposed surface of the 3D object (or any portion thereof). The sensorcan detect the amount of pre-transformed material deposited in thematerial bed. The sensor can comprise a proximity sensor. For example,the sensor may detect the amount of pre-transformed material depositedon the platform or on the exposed surface of a material bed. The sensormay detect the physical state of material deposited on the targetsurface (e.g., liquid, or solid (e.g., powder or bulk)). The sensor candetect the microstructure (e.g., crystallinity) of pre-transformedmaterial deposited on the target surface. The sensor may detect theamount of pre-transformed material disposed by the layer dispensingmechanism (e.g., powder dispenser). The sensor may detect the amount ofpre-transformed material that is relocated by the layer dispensingmechanism (e.g., by the leveling mechanism). The sensor can detect thetemperature of the powder and/or transformed material in the materialbed. The sensor may detect the temperature of the pre-transformedmaterial in a powder dispensing mechanism, and/or in the material bed.The sensor may detect the temperature of the pre-transformed materialduring and/or after its transformation. The sensor may detect thetemperature and/or pressure of the atmosphere within the enclosure(e.g., chamber). The sensor may detect the temperature of the material(e.g., powder) bed at one or more locations.

At times, the at least one sensor is operatively coupled to a controlsystem (e.g., computer control system). The sensor may comprise lightsensor, acoustic sensor, vibration sensor, chemical sensor, electricalsensor, magnetic sensor, fluidity sensor, movement sensor, speed sensor,position sensor, pressure sensor, force sensor, density sensor, distancesensor, or proximity sensor. The sensor may comprise temperature sensor,weight sensor, material (e.g., powder) level sensor, metrology sensor,gas sensor, or humidity sensor. The metrology sensor may comprise ameasurement sensor (e.g., height, length, width, angle, and/or volume).The metrology sensor may comprise a magnetic, acceleration, orientation,or optical sensor. The sensor may transmit and/or receive sound (e.g.,echo), magnetic, electronic, and/or electromagnetic signal. Theelectromagnetic signal may comprise a visible, infrared, ultraviolet,ultrasound, radio wave, or microwave signal. The metrology sensor maymeasure a vertical, horizontal, and/or angular position of at least aportion of the target surface. The metrology sensor may measure a gap.The metrology sensor may measure at least a portion of the layer ofmaterial. The layer of material may be a pre-transformed material,transformed material, or hardened material. The metrology sensor maymeasure at least a portion of the 3D object. The gas sensor may senseany of the gas. The distance sensor can be a type of metrology sensor.The distance sensor may comprise an optical sensor, or capacitancesensor. The temperature sensor can comprise Bolometer, Bimetallic strip,calorimeter, Exhaust gas temperature gauge, Flame detection, Gardongauge, Golay cell, Heat flux sensor, Infrared thermometer,Microbolometer, Microwave radiometer, Net radiometer, Quartzthermometer, Resistance temperature detector, Resistance thermometer,Silicon band gap temperature sensor, Special sensor microwave/imager,Temperature gauge, Thermistor, Thermocouple, Thermometer (e.g.,resistance thermometer), or Pyrometer. The temperature sensor maycomprise an optical sensor. The temperature sensor may comprise imageprocessing. The temperature sensor may be coupled to a processor thatwould perform image processing by using at least one sensor generatedsignal. The temperature sensor may comprise a camera (e.g., IR camera,CCD camera). The pressure sensor may comprise Barograph, Barometer,Boost gauge, Bourdon gauge, Hot filament ionization gauge, Ionizationgauge, McLeod gauge, Oscillating U-tube, Permanent Downhole Gauge,Piezometer, Pirani gauge. Pressure sensor, Pressure gauge, Tactilesensor, or Time pressure gauge. The position sensor may compriseAuxanometer, Capacitive displacement sensor, Capacitive sensing, Freefall sensor, Gravimeter, Gyroscopic sensor, Impact sensor, Inclinometer,Integrated circuit piezoelectric sensor, Laser rangefinder, Lasersurface velocimeter, LIDAR, Linear encoder, Linear variable differentialtransformer (LVDT), Liquid capacitive inclinometers, Odometer,Photoelectric sensor, Piezoelectric accelerometer, Rate sensor, Rotaryencoder. Rotary variable differential transformer, Selsyn, Shockdetector, Shock data logger, Tilt sensor, Tachometer. Ultrasonicthickness gauge, Variable reluctance sensor, or Velocity receiver. Theoptical sensor may comprise a Charge-coupled device, Colorimeter,Contact image sensor, Electro-optical sensor. Infra-red sensor, Kineticinductance detector, light emitting diode (e.g., light sensor),Light-addressable potentiometric sensor, Nichols radiometer, Fiber opticsensor, Optical position sensor, Photo detector, Photodiode,Photomultiplier tubes, Phototransistor, Photoelectric sensor,Photoionization detector, Photomultiplier, Photo resistor, Photo switch,Phototube. Scintillometer, Shack-Hartmann, Single-photon avalanchediode, Superconducting nanowire single-photon detector, Transition edgesensor, Visible light photon counter, or Wave front sensor. The weightof the material bed can be monitored by one or more weight sensors. Theweight sensor(s) may be disposed in, and/or adjacent to the materialbed. A weight sensor disposed in the material bed can be disposed at thebottom of tire material bed (e.g. adjacent to the platform). The weightsensor can be between the bottom of the enclosure (e.g., FIG. 1, 111)and the substrate (e.g., FIG. 1, 109) on which the base (e.g., FIG. 1,102) or the material bed (e.g., FIG. 1, 104) may be disposed. The weightsensor can be between the bottom of the enclosure and the base on whichthe material bed may be disposed. The weight sensor can be between thebottom of the enclosure and the material bed. A weight sensor cancomprise a pressure sensor. The weight sensor may comprise a springscale, a hydraulic scale, a pneumatic scale, or a balance. At least aportion of the pressure sensor can be exposed on a bottom surface of thematerial bed. The weight sensor can comprise a button load cell. Thebutton load cell can sense pressure from pre-transformed materialadjacent to the load cell. In an example, one or more sensors (e.g.,optical sensors or optical level sensors) can be provided adjacent tothe material bed such as above, below, or to the side of the materialbed. In some examples, the one or more sensors can sense the level(e.g., height and/or amount) of pre-transformed material in the materialbed. The pre-transformed material (e.g., powder) level sensor can be incommunication with a layer dispensing mechanism (e.g., powderdispenser). Alternatively, or additionally a sensor can be configured tomonitor the weight of the material bed by monitoring a weight of astructure that contains the material bed. One or more position sensors(e.g., height sensors) can measure the height of the material bedrelative to the platform. The position sensors can be optical sensors.The position sensors can determine a distance between one or more energybeams (e.g., a laser or an electron beam) and the exposed surface of thematerial (e.g., powder) bed. The one or more sensors may be connected toa control system (e.g., to a processor and/or to a computer).

In some embodiments, the systems and/or apparatuses disclosed hereincomprise one or more motors. The motors may comprise servomotors. Theservomotors may comprise actuated linear lead screw drive motors. Themotors may comprise belt drive motors. The motors may comprise rotaryencoders. The apparatuses and/or systems may comprise switches. Theswitches may comprise homing or limit switches. The motors may compriseactuators. The motors may comprise linear actuators. The motors maycomprise belt driven actuators. The motors may comprise lead screwdriven actuators. The actuators may comprise linear actuators. Thesystems and/or apparatuses disclosed herein may comprise one or morepistons.

In some examples, a pressure system is in fluid communication with theenclosure. The pressure system can be configured to regulate thepressure in the enclosure. In some examples, the pressure systemincludes one or more pumps. The one or more pumps may comprise apositive displacement pump. The positive displacement pump may compriserotary-type positive displacement pump, reciprocating-type positivedisplacement pump, or linear-type positive displacement pump. Thepositive displacement pump may comprise rotary lobe pump, progressivecavity pump, rotary gear pump piston pump, diaphragm pump, screw pump,gear pump, hydraulic pump, rotary vane pump, regenerative (peripheral)pump, peristaltic pump, rope pump, or flexible impeller. Rotary positivedisplacement pump may comprise gear pump screw pump, or rotary vanepump. The reciprocating pump comprises plunger pump, diaphragm pump,piston pumps displacement pumps, or radial piston pump. The pump maycomprise a valveless pump. steam pump, gravity pump, eductor-jet pump,mixed-flow pump, bellow pump, axial-flow pumps, radial-flow pump,velocity pump, hydraulic ram pump, impulse pump, rope pump,compressed-air-powered double-diaphragm pump, triplex-style plungerpump, plunger pump, peristaltic pump, roots-type pumps, progressingcavity,' pump, screw pump, or gear pump.

In some examples, the pressure system includes one or more vacuum pumpsselected from mechanical pumps, rotary vain pumps, turbomolecular pumps,ion pumps, cryopumps, and diffusion pumps. The one or more vacuum pumpsmay comprise Rotary vane pump, diaphragm pump, liquid ring pump, pistonpump, scroll pump, screw pump, Wankel pump, external vane pump, rootsblower, multistage Roots pump, Toepler pump, or Lobe pump. The one ormore vacuum pumps may comprise momentum transfer pump, regenerativepump, entrapment pump, Venturi vacuum pump, or team ejector. Thepressure system can include valves; such as throttle valves. Thepressure system can include a pressure sensor for measuring the pressureof the chamber and relaying the pressure to the controller, which canregulate the pressure with the aid of one or more vacuum pumps of thepressure system. The pressure sensor can be coupled to a control system(e.g., controller). The pressure can be electronically or manuallycontrolled.

In some examples, the systems, apparatuses, and/or methods describedherein comprise a material recycling mechanism. The recycling mechanismcan collect at least unused pre-transformed material and return theunused pre-transformed material to a reservoir of a powder dispensingmechanism (e,g, the powder dispensing reservoir), or to a bulk reservoirthat feeds the powder dispensing mechanism. The recycling mechanism andthe bulk reservoir are described in U.S. provisional patent applicationNo. 62/265,817, U.S. patent application Ser. No. 15/374,318, or PCTpatent application minter PCT/US20161066000, each of which isincorporated herein by reference in its entirety wherenon-contradictory.

In some cases, unused material (e.g., remainder) surround the 3D objectin the material bed. The unused material can be substantially removedfrom the 3D object. The unused material may comprise pre-transformedmaterial. Substantial removal may refer to material covering at mostabout 20%, 15%, 10%, 8%, 6%, 4%, 2%, 1%, 0.5%, or 0.1% of the surface ofthe 3D object after removal. Substantial removal may refer to removal ofall the material that was disposed in the material bed and remained aspre-transformed material at the end of the 3D printing process (i.e.,the remainder), except for at most about 10%, 3%, 1%, 0.3%, or 0.1% ofthe weight of the remainder. Substantial removal may refer to removal ofall the remainder except for at most about 50%, 10%, 3%, 1%, 0.3%, or0.1% of the weight of the printed 3D object. The unused material can beremoved to permit retrieval of the 3D object without digging through thematerial bed. For example, the unused material can be suctioned out ofthe material bed by one or more vacuum ports (e.g., nozzles) builtadjacent to the material bed, by brushing off the remainder of unusedmaterial, by lifting the 3D object from the unused material, by allowingthe unused material to flow away from the 3D object (e.g., by opening anexit opening port on the side(s) and/or on the bottom of the materialbed from which the unused material can exit). After the unused materialis evacuated, the 3D object can be removed. The unused pre-transformedmaterial can be re- circulated to a material reservoir for use in futurebuilds. The removal of the remainder may be effectuated as described inU.S. provisional patent application No. 62/265,817, U.S. patentapplication Ser. No. 15/374,318, or PCT patent application numberPCT/US15/36802, each of which is incorporated herein by reference in itsentirety where non-contradictoty. In some cases, cooling gas can bedirected to the hardened material (e.g., 3D object) for cooling thehardened material during and/or following its retrieval.

In some cases, a layer of the 3D object can be formed within at mostabout 1 hour (h), 30 minutes (min), 20 min, 10 min, 5 min, 1 min, 40seconds (s), 20 s, 10 s, 9 s, 8 s, 7 s, 6 s, 5 s, 4 s, 3 s, 2 s, or 1 s.A layer of the 3D object can be formed within at least about 30 minutes(min), 20 min, 10 min 5 mm, 1 min, 40 seconds (s), 20 s, 10 s, 9 s, 8 s.7 s, 6 s, 5 s, 4 s, 3 s, 2 s, or 1 s. A. layer of the 3D can be formedwithin any time between the aforementioned time scales (e.g., from about1 h to about 1 s, from about 10 min to about 1 s, from about 40 s toabout 1 s, from about 10 s to about 1 s, or from about 5 s to about 1s).

The final form of the 3D object can be retrieved soon after cooling of afinal layer of hardened material. Soon after cooling may be at mostabout 1 day, 12 hours (h), 6 h, 5 h, 4 h, 3 h, 2 h, 1 h, 30 minutes, 15minutes, 5 minutes, 240 s, 220 s, 200 s, 180 s, 160 s, 140 s, 120 s, 100s, 80 s, 60 s, 40 s, 20 s, 10 s, 9 s, 8 s, 7 s, 6 s, 5 s, 4 s, 3 s, 2 s,or 1 s. Soon after cooling may be between any of the aforementioned timevalues (e.g., from about is to about 1 day, from about 1 s to about 1hour, from about 30 minutes to about 1 day, from about 20 s to about 240s, from about 12 h to about 1 s, from about 12 h to about 30 min, fromabout 1 h to about 1 s, or from about 30 min to about 40 s). In somecases, the cooling can occur by method comprising active cooling byconvection using a cooled gas or gas mixture comprising argon, nitrogen,helium, neon, krypton, xenon, hydrogen, carbon monoxide, carbon dioxide,or oxygen. Cooling may be cooling to a handling temperature. Cooling maybe cooling to a temperature that allows a person to handle the 3Dobject.

In some embodiments, the generated 3D object requires very little or nofurther processing after its retrieval. In some examples, the diminishedfurther processing or lack thereof, will afford a 3D printing processthat requires smaller amount of energy and/or less waste as compared tocommercially available 3D printing processes. The smaller amount call besmaller by at least about 1.1, 1.3, 1.5, 2, 3, 4, 5, 6, 7, 8, 9, or 10.The smaller amount may be smaller by any value between theaforementioned values (e.g., from about 1.1 to about 10, or from about1.5 to about 5). Further processing may comprise trimming. Furtherprocessing may comprise polishing (e.g., sanding). The generated 3Dobject can be retrieved and finalized without removal of transformedmaterial and/or auxiliary features. The 3D object can be retrieved whenthe 3D object, composed of hardened (e.g., solidified) material, is at ahandling temperature that is suitable to permit its removal from thematerial bed without its substantial deformation. The handlingtemperature can be a temperature that is suitable for packaging of the3D object. The handling temperature a can be at most about 120° C., 100°C., 80° C., 60° C., 40° C., 30° C., 25° C., 20° C., 10° C., or 5° C. Thehandling temperature can be of any value between the aforementionedtemperature values (e.g., from about 720° C. to about 20° C., from about40° C. to about 5° C., or from about 40° C. to about 10° C.).

The methods and systems provided herein can result in fast and/orefficient formation of 3D objects. In some cases, the 3D object can betransported within at most about 120 min, 100 min, 80 min, 60 min 40 min30 min, 20 min, 10 min, or 5 mm after the last layer of the objecthardens (e.g., solidifies). In some cases, the 3D object can betransported within at least about 120 min, 100 min, 80 min, 60 min, 40min, 30 min 20 nun, 10 min, or 5 mm after the last layer of the objectforms (e.g., hardens). In some cases, the 3D object can be transportedwithin any time between the above-mentioned values (e.g., from about 5min to about 120 min, from about 5 mm to about 60 min, or from about 60min to about 120 min). The 3D object can be transported once it cools toa temperature of at most about 100° C., 90° C., 80° C., 70° C., 60° C.,50° C., 40° C., 30° C., 25° C., 20° C., 15° C. 10° C., or 5° C. The 3Dobject can be transported once it cools to a temperature value betweenthe above-mentioned temperature values (e.g., from about 5° C. to about100° C., from about 5° C. to about 40° C., or from about 15° C. to about40° C.). Transporting the 3D object can comprise packaging and/orlabeling the 3D object. In some cases, the 3D object can be transporteddirectly to a consumer.

In some embodiments, the methods, systems, apparatuses, and/or softwarepresented herein facilitates formation of custom or a stock 3D objectsfor a customer. A customer can be an individual, a corporation,organization, government, non-profit organization, company, hospital,medical practitioner, engineer, retailer, any other entity, orindividual. The customer may be one that is interested in receiving the3D object and/or that ordered the 3D object. A customer can submit arequest for formation of a 3D object. The customer can provide an itemof value in exchange for the 3D object. The customer can provide adesign or a model for the 3D object. The customer can provide the designin the form of a stereo lithography (STL) file. The customer can providea design Wherein the design can be a definition of the shape and/ordimensions of the 3D object in any other numerical or physical form. Insome cases, the customer can provide a 3D model, sketch, and/or image asa design of an object to be generated. The design can be transformed into instructions usable by the printing system to additively generate the3D object. The customer can provide a request to form the 3D object froma specific material or group of materials (e.g., a material as describedherein). In some cases, the design may not contain auxiliary features(or marks of any past presence of auxiliary support features).

In response to the customer request, the 3D object can be formed orgenerated as described herein. In some cases, the 3D object can beformed by an additive 3D printing process (e.g., additivemanufacturing). Additively generating the 3D object can comprisesuccessively depositing and transforming (e.g., melting) apre-transformed material comprising one or more materials as specifiedby the customer. The 3D object can be subsequently delivered to thecustomer. The 3D object can be formed without generation or removal ofauxiliary features (e.g., that is indicative of a presence or removal ofthe auxiliary support feature). Auxiliary features can be supportfeatures that prevent a 3D object from shifting, deforming or movingdating the formation of the 3D object.

The 3D object (e.g., solidified material) that is generated for thecustomer can have an average deviation value from the intendeddimensions (e.g., specified by the customer, or designated according toa model of the 3D object) of at most about 0.5 microns (μm), 1 μm, 3 μm,10 μm, 30 μm, 100 μm, 300 μm, or less. The deviation can be any valuebetween the aforementioned values (e.g., from about 0.5 μm to about 300μm, from about 10 μm to about 50 μm, from about 15 μm to about 85 μm,from about 5 μm to about 45 μm, or from about 15 μm to about 35 μm). The3D object can have a deviation from the intended dimensions in aspecific direction, according to the formula Dv +L/K_(Dv), wherein Dv isa deviation value, L is the length of the 3D object in a specificdirection, and K_(Dv) is a constant. Dv can have a value of at mostabout 300 μm, 200 μm, 100 μm, 50 μm, 40 μm, 30 μm, 20 μm, 10 μm, 5 μm, 1μm, or 0.5 μm. Dv can have a value of at least about 0.5 μm, 1 μm, 3 μm,5 μm, 10 μm, 20 μm, 30 μm, 50 μm, 70 μm, 100 μm, or 300 μm. Dv can haveany value between the aforementioned values (e.g., from about 0.5 μm toabout 300 μin, from about 10 μm to about 50 μm, from about 15 μm toabout 85 μm, from about 5 μm to about 45 μm, or from about 15 μm toabout 35 μm). K_(Dv) can have a value of at most about 3000, 2500, 2000,1500, 1000, or 500. K_(Dv) can have a value of at least about 500, 1000,1500, 2000, 2500, or 3000. K_(Dv) can have any value between theaforementioned values (e.g., from about 3000 to about 500, from about1000 to about 2500, from about 500 to about 2000, from about 1000 toabout 3000, or from about 1000 to about 2500).

The intended dimensions can be derived from a model design, The 3D partcan have the stated accuracy value immediately after its formation,without additional processing or manipulation. Receiving the order forthe object, formation of the object, and delivery of the object to thecustomer can take at most about 7 days, 6 days, 5 days, 3 days, 2 days,1 day, 12 hours, 6 hours, 5 hours, 4 hours, 3 hours, 2 hours, 1 hour, 30min, 20 min, 10 min, 5 mm, 1 min, 30 seconds, or 10 seconds. Receivingthe order for the object, formation of the object, and delivery of theobject to the customer can take a period of time between any of theaforementioned time periods (e.g., from about 10 seconds to about 7days, from about 10 seconds to about 12 hours, from about 12 hours toabout 7 days, or from about 12 hours to about 10 minutes). In somecases, the 3D object can be generated in a period between any of theaforementioned time periods (e.g., from about 10 seconds to about 7days, from about 10 seconds to about 12 hours, from about 12 hours toabout 7 days, or from about 12 hours to about 10 minutes). The time canvary based on the physical characteristics of the object, including thesize and/or complexity of the object.

In some embodiments, the system and/or apparatus comprises a controllingmechanism (e.g., a controller). The methods, systems, apparatuses,and/or software disclosed herein may incorporate a controller thatcontrols one or more of the components described herein. The controllermay comprise a computer-processing unit (e.g., a computer) coupled toany of the systems and/or apparatuses, or their respective components(e.g., the energy source(s)). Alternatively, or additionally, thesystems and/or apparatuses disclosed herein may be coupled to aprocessing unit. Alternatively, or additionally, the methods mayincorporate the operation of a processing unit. The computer can beoperatively coupled through a wired and/or through a wirelessconnection. In some cases, the computer can be on board a user device. Auser device can be a laptop computer, desktop computer, tablet,smartphone, or another computing device. The controller can be incommunication with a cloud computer system and/or a server. Thecontroller can be programmed to selectively direct the energy source(s)to apply energy to the at least a portion of the target surface at apower per unit area. The controller can be in communication with thescanner configured to articulate the energy source(s) to apply energy toat least a portion of the target surface at a power per unit area.

At times, the controller controls the layer dispensing mechanism and/orany of its components. The controller may control the platform. Thecontroller may control the one or more sensors. The controller maycontrol any of the components of the 3D printing system and/orapparatus. The controller may control any of the mechanisms used toeffectuate the methods described herein. The control may comprisecontrolling (e.g., directing and/or regulating) the speed (velocity) ofmovement of any of the 3D printing mechanisms and/or components. Themovement may be horizontal, vertical, and/or in an angle (planar and/orcompound). The controller may control at least one characteristic of thetransforming energy beam. The controller may control the movement of thetransforming energy beam (e.g., according to a path). The controller maycontrol the source of the (transforming) energy beam. The energy beam(e.g., transforming energy beam, or sensing energy beam) may travelthrough an optical setup. The optical setup may comprise a mirror, alens, a focusing device, a prism, or an optical window.

At times, the controller controls the level of pressure (e.g., vacuum,ambient, or positive pressure) in the powder removal mechanism powderdispensing mechanism, and/or the enclosure (e.g., chamber). The pressurelevel (e.g., vacuum, ambient, or positive pressure) may be constant orvaried. The pressure level may be turned on and off manually and/or bythe controller. The controller may control at least one characteristicand/or component of the layer dispensing mechanism. For example, thecontroller may control the direction and/or rate of movement of thelayer dispensing mechanism and any of its components. The controller maycontrol the cooling member (e.g., external, and/or internal). Themovement of the layer dispensing mechanism or any of its components maybe predetermined. The movement of the layer dispensing mechanism or anyof its components may be according to an algorithm. Other controlexamples can be found in U.S. provisional patent application No.62/265,817, U.S, patent application Ser. No. 15/374,318, or PCT patentapplication number PCT/US15/36802, each of which is incorporated hereinby reference in its entirety where non-contradictory. The control may bemanual and/or automatic. The control may be programmed and/or beeffectuated a whim. The control may be according to an algorithm. Thealgorithm may comprise a printing algorithm, or motion controlalgorithm. The algorithm may consider the model of the 3D object.

In some embodiments, properties (e.g., density and/or surface roughness)of a hardened material formed from a first transformation operation(e.g., an STO or PMX process) can be modified by implementing a secondtransformation operation performed of that hardened material. The secondtransformation operation (e.g., process) can transform one layer ofhardened material at a time, or transform a plurality of layers hardenedmaterial, e.g., depending on how deep the second transformation canpenetrate and transform (e.g., remelt) the material. The penetration ofthe second transformation across one or more layers of hardened materialmay depend on the power density of the energy beam, and/or the materialproperties (e.g., heat conductivity) of the hardened material. In someexamples, a HARMP process can be used to transform a depth of hardenedmaterial. The depth may correspond to the depth the generated HARMP meltpool. The HARMP formed melt pool may be (e.g., substantially) devoid of(e.g., detectable) pores. In some embodiments, a HARMP process isimplemented on a hardened material that is generated by a 3D process orby a different methodology (e.g., that has a thickens of at least about100 μm-1000 μm). The different methodology may comprise casting,molting, or welding. In some embodiments, the HARMP process is a secondtransformation operation. The HARMP process can be implemented on about10-15 layers (e.g., about 500-1000 μm) of hardened material (e.g.,generated from a first transformation process of a 3D printing, e.g., asdescribed herein). In some embodiments, the second transformationoperation transforms at least about 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12,13, 14, 15, 16, 18, 19, or 20 layers of hardened material (e.g., thatare generated by a first transformation operation of a 3D printingprocess). The second transformation operation may transform a number oflayers between any of the afore-mentioned number of layers of hardenedmaterial (e.g., from about 2 to about 15 layers, from about 2 layers toabout 10 layers, or from about 10 layers to about 20 layers of hardenedmaterial), in some embodiments, the second transformation operationtransforms a hardened material having vertical height of at least 100micrometers (μm), 200 μm, 300 μm, 400 μm, 500 μm, 600 μm, 700 μm, 800μm, 900 μm, or 1000 μm of hardened material (e.g., that are generated bythe first transformation operation). The second transformation operationcan transform a vertical height of hardened material layers between anyof the afore-mentioned values (e.g., from about 100 μm to about 1000 μm,from about 100 μm to about 500 μm, or from about 500 μm to about 1000 μma vertical height of hardened material). The aspect ratio of the meltpool of the second transformation process (e.g., HARMP) can by any ofthe high aspect ratio melt pool values described herein. The hardenedmaterial that is submitted for second transformation can have a lowerdensity than the hardened material that results from the secondtransformation. The hardened material that is submitted for the secondtransformation operation can have any of the density values describedherein for the first density. For example, a maximum density value rangespanning from about 60% to about 80% (v/v, or area/area porosity, e.g.,of a cross-section plane of maximum porosity). The hardened materialthat is generated after the second transformation operation can have anyof the density values described herein for the denser structure of forthe second density. For example, the hardened material that underwentthe second transformation operation can be at least 99.5% or 99.9% densev/v, or area/area porosity, e.g., of a cross-section plane of maximumporosity).

FIG. 34A shows an example of a vertical cross-sectional image of ahardened material portion as part of a 3D object formed using a firsttransformation operation, in accordance with some embodiments (e.g.,using the STO methodology to form each layer), indicating a plurality ofpores. FIG. 34B shows an example of a vertical cross-sectional image ofa hardened material portion as part of a 3D object formed using a firsttransformation operation followed by a second transformation operation,in accordance with some embodiments (e.g., wherein each layer was formedusing the STO methodology followed by using a HARMP methodology),indicating an absence of pores. In the examples shown in each of FIGS.34A and 34B, the hardened material has a thickness of about 600 μm. Asshown in the example of FIG. 34A, pores (e.g., 3400) form within thehardened material. In some cases, the pores have diameters rangingbetween about 20 to about 200 μm. The pores can have a random or (e.g.,substantially) ellipsoidal shape, e.g., globular shape. Note that in theexample shown in FIG. 34A, the melt pool edges (e.g., 3402) aredetectable, as well as the exposed surface 3404 (e.g., outer surface) ofthe hardened material. After the second transformation operation, thehardened material can have substantially no (e.g., detectable) pores,e.g., pores that are greater than about 20 μm. FIG. 34B shows highaspect ratio melt pool (HARMP) having edges (e.g., 3406) as part of thehardened material having an exposed surface 3408. FIG. 35A shows anexample of a horizontal X-ray image of a hardened material of a 3Dobject 3500 formed using a first transformation operation, in accordancewith some embodiments (e.g., using the STO mythology to form eachlayer), indicating a plurality of pores depicted as bright dots (e.g.,3502). The 3D object shown in FIG. 35A comprises an auxiliary supportstructure portion 3509 and a sloping ledge portion 3510. FIG. 35B showsan example of a horizontal X-ray image of a hardened material portion aspart of a 3D object formed using a first transformation operationfollowed by a second transformation operation, in accordance with someembodiments (e.g., wherein each layer was formed using the STO mythologyfollowed by using a HARMP methodology), indicating an absence ofdetectable pores. The 3D object 3503 shown in FIG. 35C comprises anauxiliary support structure portion 3505 and a sloping ledge portion3507. In the X-ray images shown in FIGS. 35A and 35C, the darker grayshaded areas (e.g., 3504) represent denser material portions than thelighter areas (e.g., 3502, pointing to a pore).

In some embodiments, the second transformation operation can modify thesurface texture and/or roughness of a hardened material. FIG. 35B showsan example of a topological top view image of a hardened material of a3D object 3506 formed using a first transformation operation, inaccordance with some embodiments (e.g., using the STO mythology to formeach layer), indicating an oscillating exposed surface structure. Thetop view image of the hardened material 3506 shown in FIG. 35Bcorresponds to a fraction of the ledge portion 3510 shown as an X-rayimage in. FIG. 35A. FIG. 35D shows an example of a topological top viewimage of a hardened material portion as part of a 3D object formed usinga first transformation operation followed by a second transformationoperation, in accordance with some embodiments (e.g., wherein each layerwas formed using the STO mythology followed by using a HARMPmethodology), indicating smoother surface as compared to the one shownin FIG. 35B. The topological top view image of the hardened material3508 shown in FIG. 35D corresponds to a fraction of the ledge portion3507 shown as an X-ray image in FIG. 35C. In the topological imagesshown in FIGS. 35B and 35D, the gray scale represents height variations.In the example shown in FIG. 35B, a roughness of the exposed surface3506 is measured and indicated in terms of average Sa value (thearithmetic average of the roughness profile extended to a surface) ofabout 18 μm. In FIG. 35D, the exposed surface has a reduced surfaceroughness that is measured and indicated in terms of an Sa of about 17μm.

In some embodiments, the second transformation is repeated in aplurality of 3D printing cycles with (i) reproducible, (ii) consistent,and/or (iii) homogenous results, e.g., in terns of deviation from arequest shape of the 3D object, material properties (e.g., density,and/or strength), and exposed surface roughness, or any combinationthereof. The strength can be tensile strength. In some embodiments, aplurality of 3D printing cycles generates 3D objects that have (i)reproducible. (ii) consistent, and/or (iii) homogenous properties, e.g.,in terms of deviation from a request shape of the 3D object, materialproperties (e.g., density, and/or strength), exposed surface roughness,or any combination thereof. The strength can be tensile strength. Insome embodiments, the plurality of 3D printing cycles (e.g., using thesecond transformation) can generate (e.g., substantially) the same 3Dobject properties in at least 5, 10, 25, or 50 separately printed parts(e.g., printed in separate print cycles), which properties comprise (I)deviation from a request shape of the 3D object, (II) materialproperties (e.g., density, and/or strength), or MO exposed surfaceroughness. In some parts, the second transformation can be used on anextended ledge, cavity ceiling, undercut, and/or structure (or a portionthereof) that is not anchored to a base. For example, the one or morelayers of hardened material can be part of a horizontal non-overlappingportion of the part (e.g., such as portions of an extended ledge. SeeFIG. 30B, a non-overlapping portion of the second bottom skin layer3020). Such structures can be constrained structures (e.g., having abottom skin layer). The second transformation operation can be performedto further densify the hardened material without, for example, deforming(e.g., via roughening and/or warping) portions (e.g., bottom skins) ofthe ledge, ceiling, undercut, and/or non-anchored structure. In someembodiments, the second transformation comprises a STO tiling process.In some embodiments, the second transformation comprises a HARMPprocess.

In some aspects, further densifying the hardened material (e.g., in situand/or in real time) includes (i) using a first transformation operationto form a first hardened material having one or more layers thatcomprise pores (e.g., at most about 70%, 80%, or 90% dense (v/v, orarea/area porosity, e.g., of a. cross-section plane of maximumporosity)), (ii) optionally placing a pre-transformed material (e.g.,powder) layer on the first hardened material, and (iii) using a secondtransformation operation to apply energy to the first hardened material(and optionally simultaneously transform the pre-transformed materiallayer to a transformed material) to form a second hardened material thathas a higher density (e.g., at least about 95% or 99.9% dense (v/v. orarea/area porosity, e.g., of a cross-section plane of maximum porosity))and/or lower surface roughness (e.g., Ra of at most 20 μm or 40 μm) ascompared to the first hardened material. In some embodiments, the addedpre-transformed material (e.g., powder) layer in (ii) can be used tocompensate for a volume contraction during the transformation process(e.g., due to elimination of pores). In some cases, the addedpre-transformed material layer is utilized to increase a volume (e.g.,height) of the first hardened material when generating the secondhardened material. In some embodiments, the added pre-transformedmaterial layer in (ii) can he used to increase the volume (e.g., height)of the second hardened material as compared to the first hardenedmaterial. In some cases, the first transformation operation transformsthe pre-transformed to form a low-density level of hardened material(e.g., powder) (e.g., a density from about 30% to about 60% density) toa moderate density level of hardened material (e.g., a density fromabout 70% to about 90% density). The second transformation operation maydensity one or more layers of the moderate density material to a highly(e.g., fully) dense material (e.g., having a density of at least 95%).The density percentages are calculated v/v, or area/area porosity, e.g.,of a cross-section plane of maximum porosity. In some cases, at least aportion of the 3D object is gradually densified. For example, the atleast a portion of the 3D object is generated as a low density hardenedmaterial, which is subsequently densified to a high density hardenedmaterial. For example, the at least a portion of the 3D object isgenerated as an intermediate density hardened material, which issubsequently densified to a high density hardened material. In somecases, at least a portion of the 3D object is gradually densified. Forexample, the at least a portion of the 3D object is generated as a lowdensity hardened material, which is subsequently densified to anintermediate density hardened material, which is subsequently densifiedto a high density hardened material. Gradually densifying the 3D object(e.g., in a plurality of transformation operations) to form a fullydense material can facilitate generation of the requested complex 3Dobject (e.g., comprising extended ledges, cavity ceilings, undercutgeometries) with minimal post processing procedures (e.g., or lackthereof). For example, the complex 3D object (or complex portionsthereof) may be generated (i) without being anchored (e.g., to thebase), and/or (ii) with low degree of dimensional deviation from therequested 3D object (or lack thereof), e.g., with negligible deformation(or lack thereof). In some cases, the second transformation can beimplemented through a depth spanning a plurality of layers of hardenedmaterial (e.g., and optionally one or more layer of pre-transformedmaterial). In some applications, the fully dense hardened materialbottom skin layer is capable of supporting formation of an additionalstructure that is (i) heavier than the bottom skin layer, (ii) morevoluminous than the bottom skin layer, and/or (iii) denser than thebottom skin layer. The additional structure may comprise core or PMX.

In some embodiments, the 3D process comprises a plurality oftransformation methodologies (e.g., processes). The varioustransformation processes described herein can be used in any combinationsuitable for accomplishing particular application requirements. Forinstance, in some embodiments, a HARMP process is used in or after amulti-transformation operation (MTO). In some embodiments, the HARMPprocess is used to transform an overhang structure of a 3D object. FIGS.43A-43C show top views of example layers of 3D objects having overhangstructures undergoing MTO processes that include HARMP. FIG. 43A showshorizontal (e.g., top or bottom views) examples of a layer 4300 having acore portion 4302 and an overhang portion 4304. The core (e.g., rigid)portion can be formed using a hatching process, thereby forming multiplehatches (e.g., 4308). During a first transformation operation, theoverhang portion can be formed using a tiling process to form (e.g.,substantially) overlapping or non-overlapping adjacent tiles (e.g.,4306). The tiles may be formed successively. The successive tiles may beadjacent tiles. The tiles can be formed using any tiling processdescribed herein. In some embodiments, (successive and) adjacent tilesare in contact with each other. In some embodiments, (successive and)adjacent tiles do not (e.g., substantially) contact each other. A secondtransformation operation (e.g., indicated by arrow 4310) can be used tore-transform (e.g., re-melt) at least a portion of the tiles (e.g., 4306depicting a tile). In some embodiments, the second transformationoperation comprises a HARMP operation, a hatch operation, or a secondtiling operation (e.g., along the direction of arrow 4310). The secondtransformation operation can be applied on the entire layer of hardenedmaterial, or on a portion thereof (e.g., the overhang portion, e.g.,4310, 4330, or 4350). The second transformation operation may facilitatealtering the microstructure of the secondly transformed portion.Altering may comprise altering: a grain (e.g., crystal) structure,percentage of porosity, hardness, metallurgical microstructure, meltpool size direction and/or aspect ratio, direction of epitaxial growthof the grain (e.g., crystal), or surface roughness. In some embodiments,the second transformation operation decreases a porosity and/or asurface roughness of the overhang portion (e.g., 4304) formed during thefirst transformation. FIG. 43B shows a layer 4320 having a core portion4322 and an overhang portion 4324. The core portion can be formed usinga hatching process, thereby forming multiple hatches (e.g., 4328).During a first transformation operation, the overhang portion (e.g.,4324) can be formed using a hatching process to form overhang hatches(e.g., 4326). The overhang hatches can be formed using any hatchingprocess. A second transformation operation (e.g., indicated by arrow4330) can be used to re-transform (e.g., re-melt) at least a portion ofthe overhang hatches (e.g., 4326). The second transformation operationcan use the same or a different type of transformation operation. Forexample, the first and second transformation can use hatching. Forexample, the first transformation may use hatching, and the secondtransformation may use tiling. For example, the first transformation mayuse tiling and the second transformation may use HARMP. In someembodiments, the second transformation operation decreases a porosityand/or a surface roughness of the overhang portion (e.g., 4324) formedfrom the first transformation. FIG. 43C shows a layer 4340 having a coreportion 4342 and an overhang portion 4344. The core portion can beformed using a hatching process, thereby forming multiple hatches (e.g.,4348). During a first transformation operation, the overhang portion(e.g., 4344) can be formed using a tiling process to form overlappingtiles (e.g., 4346) (also referred to as a “densely tiled” region). Thetiles can be formed using any tiling process described herein. In someembodiments, at least some of the adjacent tiles (e.g., substantially)completely overlap with each other. A second transformation operation(e.g., indicated by arrow 4:350) can be used to re-transform (e.g.,re-melt) at least a portion of the tiles (e.g., 4346).

An overhang can be formed in a way that connects the overhang to an edgeof a previously transformed (e.g., hardened) segment of the 3D object.The transformation can comprise moving (e.g., scanning) the energy beamalong the edge. The transformation can comprise moving (e.g., scanning)the energy beam at an angle with respect to the edge (e.g., 45 degreesor 90 degrees with respect to the edge). The energy beam (e.g., a centerof the energy beam) can be on or sufficiently proximate to the edge tore-transform at least a portion of the previously transformed (e.g.,hardened) segment of the 3D object at or immediately adjacent to thepreviously formed edge as part of a previously formed layer of hardenedmaterial. The transformation can include any type of transformationprocess described herein (e.g., tiling, hatching, type-1 energy beam,type-2 energy beam, PMX, MTO and/or STO). The FIGS. 44A-44C show topviews of example layers of 3D objects undergoing various transformationprocesses for forming overhang structures. FIG. 44A shows an example ofa previously transformed (e.g., hardened) segment 4402 of a 3D objecthaving an edge 4404 undergoing a transformation (e.g., printing)operation for forming an overhang. During the transformation operation,at least a portion of the energy beam may be directed at the edge (e.g.,4404) and on a pre-transformed material (e.g., that is a part of amaterial bed, e.g., 4408). In some embodiments, the previouslytransformed segment (e.g., 4402) is covered by one or more layers ofpre-transformed material during the transformation. In some embodiments,the previously transformed segment (e.g., 4402) is exposed (e.g., notcovered by one or more layers of pre-transformed material) during thetransformation. The energy beam can be scanned along the edge inaccordance with a path (e.g., 4406). The energy beam may transform thepre-transformed material and m-transform at least a portion of thepreviously transformed segment in accordance with the path. The path maybe in a direction (e.g., 4410) along the edge (e.g., 4404). The path maybe from a first location (e.g., 4412) to a second location (e.g., 4414)along the edge (e.g., 4404). FIG. 44B shows an example of a previouslytransformed (e.g., hardened) segment 4422 of a 3D object having an edge4424 undergoing a transformation (e.g., printing) operation for formingan overhang, a first location of the energy beam 4432, a collectivedirection of energy beam translation 4430 along a path 4426, a second(e.g., end) location of the energy beam 4434, and a material bed 4428.FIG. 44C shows an example of a previously transformed (e.g., hardened)segment 4442 of a 3D object having an edge 4444 undergoing atransformation (e.g., printing) operation for forming an overhang, afirst location of the energy beam 4452, a collective direction of energybeam translation 4450 along a path 4444, a second (e.g., end) locationof the energy beam 4454, and a material bed 4448. In some embodiments,the 3D object is not formed in a material bed, and 4408, 4428, and 4448may represent a platform. The scanning trajectory of the energy beam maytraverse parallel to the edge (e.g., 4404). The scanning trajectory maybe composed of a plurality of tiles (e.g., formed by a step and repeat,or stamping operation) that collectively traverse (e.g., ran, e.g.,4410) parallel to the edge, e.g., the path of tiles may traverse alongthe edge. The scanning trajectory may be composed of a plurality ofsmaller trajectories (e.g., hatches) each of which forming an angle withthe edge, and collectively traverse (e.g., run) parallel to the edge,e.g., the path of hatches may traverse along the edge.

In some embodiments, the overhang is formed by moving the energy beam ina direction that is different than the direction of the overallprogression along the path for at least part of a transformation process(e.g., forming path segments). FIG. 45 shows an example of a top view ofa previously transformed (e.g., hardened) segment 4502 of a 3D objecthaving an edge 4504 undergoing a transformation (e.g., printing)operation for forming an overhang. The overall path (e.g., trajectory)of the energy beam may be in accordance with a first direction (e.g.,4510) along the edge (e.g., 4504). At least part of the path (alsoreferred to herein as a sub-path) can include directing the energy beamin a second direction (e.g., 4512) that is non-parallel with the firstdirection to form path segments (e.g., 4520). In some embodiments, thesecond direction is (e.g., substantially) orthogonal to the firstdirection. In some embodiments, the second direction (e.g.,substantially) forms an acute or obtuse angle with the first direction.In some embodiments, the second direction is from the previouslytransformed segment (e.g., 4502) toward the edge (e.g., 4504), to theedge, passed the edge and/or to the pre-transformed material (e.g.,powder), e.g., of the material bed (e.g., 4508). The distance (e.g., D₁)that the energy beam travels in the second direction (e.g., 4512) andthe distance (e.g., D₂) between the sub-paths can vary. The distances D₁and D₂ can be measured from centers of the energy beam footprint (e.g.,irradiation spot) at the target surface. In some embodiments, thedistance (e.g., D₁) traveled by the energy beam in the second directionand/or the distance (e.g., D₂) between sub-paths is less than an FLS(e.g., beam diameter) of the energy beam. D₁ may be a shortest distancebetween a start position (e.g., 4521) and finish position (E.g., 4522)of the path segment. In some embodiments, the distance (e.g., D₁)traveled by the energy beam in the second direction and/or the distance(e.g., D₂) between sub-paths is (e.g., substantially) equal to orgreater than an FLS (e.g., beam diameter) of the energy beam. In someembodiments, the distance (e.g., D₁) traveled by the energy beam in thesecond direction is at least about 10 micrometers (μm), 20 μm, 30 μm, 40μm, 50 μm, 60 μm, 70 μm, 80 μm, 90 μm, 100 μm, 150 μm, 200 μm, 250 μm,300 μm, 400 μm, or 500 μm. The distance the distance (e.g., D₁) traveledby the energy beam in the second direction can range between any of theaforementioned values (e.g., from about 10 μm to about 500 μm, fromabout 10 μm to about 100 μm, from about 100 μm to about 500 μm, or fromabout 50 μm) to about 200 μm). In some embodiments, the distance e.g.,D₂) between sub-paths is at least about 10 μm, 20 μm, 30 μm, 40 μm, 50μm, 60 μm, 70 μm, 80 μm , 90 μm, 100 μm, 150 μm, 200 μm, 250 μm, 300 μm,400 μm, 500 μm, 600 μm, 700 μm, 800 μm, 900 μm, or 1000 μm. The distancee.g., D₂) between sub-paths can range between any of the afore-mentionedvalues (e.g., from about 10 μm to about 1000 μm, from about 10 μm toabout 300 μm, from about 300 μm to about 1000 μm, or from about 20 μm toabout 250 μm). The direction of the sub-path (e.g., path sections orpath segments) may be in any direction relative to the edge. FIGS.46A-46C show top view examples of 3D objects undergoing transformationoperations for forming overhangs. FIG. 46A shows a previouslytransformed (e.g., hardened) segment 4602 having an edge 4604 undergoinga transformation operation for forming an overhang. The path of theenergy beam may be in accordance with a first direction (e.g., 4610)along the edge (e.g., 4604). A sub-path of the energy beam can be in asecond direction (e.g., 4612) that is non-parallel with the firstdirection. The second direction can be from the pre-transformed material(e.g., powder) of the material bed (e.g., 4608) toward the edge (e.g.,4604) and/or the previously transformed segment (e.g., 4602). FIG. 46Bshows a previously transformed (e.g., hardened) segment 4622 in amaterial bed 4628 and having an edge 4624 undergoing a transformationoperation for forming an overhang. The path of the energy beam may be inaccordance with a first direction (e.g., 4630) along the edge (e.g.,4624). A sub-path of the energy beam can be in a second direction (e.g.,4632) that is (e.g., substantially) parallel with the first direction.In some cases, the second direction of at least one of the sub-paths is(e.g., substantially) the same as the first direction. In some cases,the second direction of at least one of the sub-paths is (e.g.,substantially) opposite the first direction. FIG. 46C shows a previouslytransformed (e.g., hardened) segment 4645 in a material bed 4642 andhaving an edge 4644 undergoing a transformation operation for forming anoverhang. The path of the energy beam may be in accordance with a firstdirection (e.g., 4650) along the edge (e.g., 4644). In some cases, asecond direction of at least one of the sub-paths is non-parallel andnon-orthogonal to the first direction. In some cases, the sub-path is azig-zag, serpentine, cross-over shape. In some, embodiments, thesub-path has a shape in accordance with one or more of the paths, e.g.,310-316 of FIG. 3.

Once an object is removed from a printer, the object may includeidentifying one or more characteristics that indicate the orientation ofthe object dining its formation in the printer. For example, the objectmay include features (e, g., transition lines, surface steps, melt poolsand/or grain boundaries) that indicate one or more (e.g., average)layering planes. In some cases, the object includes features related tothe support member(s) (e.g., FIG. 41A, 4101; or FIG. 41B, 4121) that:may or may not anchor the object to the platform (e.g., base) duringits printing. The support member(s) may be (e.g., chemically and/orphysically) bonded with the object and/or platform (e.g., base) duringprinting. FIG. 51A shows an example of a vertical cross section of a 3Dobject that includes a main portion 5100 coupled with a support member5103. The main portion (can include multiple layers (e.g., 5101 and5102) that were sequentially added during a printing operation. Thesupport member (e.g., auxiliary support) may be printed or may be theplatform (e.g., base) itself. In some embodiments, the portion of therequested 3D object comprises (e.g., substantially) the same material asthe support member. In some embodiments, the portion of the requestedobject comprises different material than the support member. Some or(e.g., substantially) all the support members may be removed from themain portion (e.g., after the printing is complete). In some cases, thesupport member causes one or more layers of the portion of the requestedobject to deform during printing (e.g., due to the presence of thesupport member during formation of the requested 3D object). Sometimes,the deformed layers comprise a visible mark. The mark may be a region ofdiscontinuity in the layer, such as a microstructure discontinuityand/or an abrupt microstructural variation. The discontinuity in themicrostructure may be explained by an inclusion of a foreign object(e.g., the support member). The microstructural variation may include(e.g., abruptly) altered melt pools and/or grain structure (e.g.,crystals, e.g., dendrites) at or near the attachment point of thesupport member. The microstructure variation may be due to differentialthermal gradients due to the presence of the support member. Thediscontinuity may be external at the surface of the 3D object. Thediscontinuity may arise flora inclusion of the support member to thesurface of the 3D object (e.g., and may be visible as a breakage of thesupport member when at attempt is made to remove the support memberafter the printing). Breakage may be the result of cutting, shaving,chipping, sawing, polishing, sanding, or any combination thereof (e.g.,to remove the support member from the main portion). In some instances,the object includes two or more support members and/or support marks.The two or more support members and/or support marks can be used todefine a build plane that is (e.g., substantially) parallel to theplatform surface during printing. In some embodiments, the build planeis (e.g., substantially) parallel to the (e.g., average) layering plane.

In some embodiments, the process used for printing at least a portion ofthe 3D object leaves one or more surface marks. The surface mark(s) maycomprise (i) a surface marking characteristic of a top surface, (ii) asurface marking characteristic of a top surface, or (iii) a surfacemarking characteristic of a side surface. The characteristic maycomprise a roughness, material deposition trajectory pattern,tessellation pattern, or auxiliary support(s) or mark(s) indicativethereof.

For example, a way of determining an orientation of an object duringprinting relates to surface roughness of the 3D object. The surfaceroughness may be an indication of the type of printing process (e.g.,hatching, tiling, HARMP, MTO, PMX, and/or STO) used to form a region ofthe object. For example, a bottom skin of an overhang (e.g., FIG. 41A,4102; or FIG. 41B, 4122) may have a different surface roughness than askin along a non-overhang portion of an object. In some cases, thebottom skin (e.g., as oriented during the printing) has a higher surfaceroughness than other skin regions of the object. In some cases, the topskin (e.g., as oriented during the printing) has a lower surfaceroughness than other skin regions of the object. Thus, the differingsurface roughness can indicate the orientation of the object withrespect to a support member (e.g., FIG. 41A, 4101; or FIG. 41B, 4121),the platform surface and/or the (e.g., average) layering plane, duringthe printing of the object.

For example, a way of determining orientation of an object duringprinting relates to the energy beam path (e.g., as instructed by thecontroller(s)). For example, a change in a direction of a hatching pathmay result in a corresponding change in the orientation of the hatch(es)in or on the object. In some cases, the hatches are in a pattern (e.g.,a checker board and/or stripe pattern) which may be visible by eye orusing imaging techniques (e.g., microscope). In some instances, theobject includes lines corresponding to borders between tessellations(which may correspond to geometric shapes used in computer modeling ofthe object and translated to the printing instruction of the object).Such patterns and/or tessellations may indicate the orientation of thelayers of the object.

In some cases, a 3D object includes one or more features that may beindicative of the process(es) used to form the 3D object. The featuresmay be microstructure features, which are very small features (e.g., asrevealed by imaging techniques such as various microscopies, e.g., asdisclosed herein). In some cases, the microstructure features influenceand/or dictate physical properties of the 3D object, such as strength,toughness, ductility, hardness, corrosion resistance, thermalconductivity and/or wear resistance. The microstructure features mayinclude melt pools, metallurgical microstructures, grain (e.g., crystal)structures and/or material phases metallurgical microstructures cancomprise cells or dendrites. The shape, size and/or orientation of themicrostructure features may be influenced by and/or indicative of thetransformation (e.g., melting) process. For example, the size and/orshape of a melt pool may at least partially depend on the power densityand/or dwell time of the energy beam at the target surface. The grain(e.g., crystal) structure, material phase, and/or metallurgicalmicrostructure can at least partially depend on the solidificationand/or cooling dynamics associated with the transformation process. Forexample, the type, size, shape and/or orientation of the microstructuresmay be influenced by thermal gradients in the molten material and/or therate in which the molten material cools. In some cases, differentprocess conditions (e.g., energy beam power and/or dwell time) result indifferent microstructures. For instance, in some cases using a type-2(tiling) energy beam having a lower power density (e.g., and irradiatingfor a longer amount of time) at a location may result in microstructuresassociated with slower cooling compared to microstructures resultingfrom using a type-1 (hatching) energy beam having a higher power density(e.g., and irradiating for a shorter amount of time) at a location. Insome cases, a slower hardening rate (e.g., solidification rate, e.g.,associated with a cooling rate) is associated with larger and/or moredefined microstructure (e.g., larger crystals (e.g., dendrites)). Thecooling rate may correspond to a hardening rate of the hardenedmaterial. In some cases, a slower cooling rate promotes formation of onealloy type and/or grain (e.g., crystal) structure rather than anotherformed by relatively quicker cooling. In some cases, the transformationprocess causes nonequilibrium hardening (e.g., solidification) of thetransformed (e.g., molten) material. The nonequilibrium hardening mayresult in formation of a nonequilibrium phase in the hardened material(e.g., that is typical for the material that is being transformed and/orhardened).

In some cases, the microstructure features are arranged with respect tothe orientation of the layers of the 3D object. For example, themicrostructure features may be oriented with respect to a (e.g.,average) layering plane of the 3D object. FIG. 49 shows an example of avertical section view of a portion of a 3D object 4900, including anexterior surface 4901 of the object. The 3D object can include aplurality of layers (e.g., 4903 or 4905) of hardened material that aresequentially stacked. The stacked layers can be bound together to form ashape of the 3D object. At least one of the layers can define a (e.g.,average) layering plane (e.g., 4914), which can indicate the orientationof the object with respect to the build platform on which the object wasformed. The layering plane may be formed during the printing of theobject due to layerwise deposition of material to generate the object.In some cases, the (e.g., average) layering plane can be defined by aboundary between two adjacent layers. The layering plane can be (e.g.,substantially) parallel to the (e.g., top) surface of the buildplatform, the exposed surface of a material bed (when present), and/or anormal to the direction of the gravitational field. The 3D object caninclude melt pools (e.g., 4906, 4908, or 4909). In some embodiments, atleast a portion of the melt pools in different layers are (e.g.,substantially) aligned with respect to an alignment line (e.g., 4912).The alignment line can be part of a plane. The alignment line may beparallel to the surface of the 3D object. The surface may be planar ornon-planar. The line may be straight or comprise a curvature. Thesurface can be non-planar Aligned melt pools in different layers can bereferred to as having inter-layer alignment (e.g., 4908 and 4909). Insome embodiments, when a side of two or more layers is aligned, the meltpools at the edge of the sides of the two or more layers are aligned. Insome cases, melt pools of a plurality of adjacent layers (e.g., 3, 4, 5,6, 7, 8, 9, 10, 15, 20, 25 or 30 adjacent layers) are (e.g.,substantially) aligned, e.g., when the edges of the layers are alignedand/or these melt pools are at an edge of these sides. FIG. 40 shows anexample of a layer 4903 having melt pool 4951 at its edge, and a layer4905 that has melt pool 4952 at its edge; the layers 4903 and 4905 analigned at side 4901 (that forms a plane); and the melt pools 4951 and4952 are aligned with respect to each other and with respect to the side4901. At least a portion (e.g., centers) of the melt pools may be (e.g.,substantially) parallel with respect to an alignment line (e.g., 4912)and/or plane 4901. The alignment line can be at any angle with respectto a (e.g., average) layering plane (e.g., 4914). In some embodiments,the alignment line is (e.g., substantially) orthogonal to the (e.g.,average) layering plane. In some embodiments, the alignment line is(e.g., substantially) parallel to at least a portion of the exteriorsurface (e.g., 4901) of the object. The alignment line may be part of analignment plane.

In some embodiments, the aligned melt pools form a skin (e.g., 4904) ofthe object. The skin can be coupled with (e.g., chemically (e.g.,metallically) bonded) an interior portion (also referred to as a core)(e.g., 2902). In some embodiments, the melt pools of the skin havewidths that span a thickness (e.g., 4911) of the skin. The thickness ofthe skin may vary depending on the application (e.g., function) of theobject. In some embodiments, the skin has a thickness of at least about20 micrometers (μm), 50 μm, 70 μm, 100 μm, 200 μm, 300 μm, 400 μm, 500μm, 600 μm, 700 μm, 800 μm, 900 μm, 1000 μm or about 2000 μm. Thethickness of skin can range between any of the afore-mentioned values(e.g., from about 20 μm to about 1000 μm, from about 20 μm to about 200μ, from about 100 μm to about 500 μm, from about 500 μm to about 1000μm, or from about 200 μm to about 400 nm). The skin may be (e.g.,directly) adjacent to a core (also referred to herein as an interiorportion) of the object. The skin may be chemically (e.g., metallically)bonded with the core (e.g., rigid portion). In some cases, a border(e.g., 4910) separates the skin from the internal portion. The core caninclude a melt pools (e.g., 4906) that are not (e.g., substantially)aligned misaligned with the alignment line and/or plane (e.g., 4912).The core melt pools may be more randomly oriented than the skin meltpools. The core melt pools may have larger distribution of sizes (e.g.,widths and/or depths) than the skin melt pools. The melt pools within aportion of the 3D object (e.g., its skin) can be more uniform in size,shape and/or alignment as compared to the melt pools in another portionof the 3D object (e.g., the core). The orientation of the melt pool andtheir relative alignment within the layer and between layers may beindicative of the process used to form them. At times, a border may formbetween microstructures (e.g., melt pools) indicative of differentformation processes. In some embodiments, a portion of the 3D object(e.g., the skin) has melt pools with sizes and/or shapes in accordancewith a tiling, hatching, STO, MTO, or HARMP operation. FIG. 50 shows anexample vertical cross-section view of a portion of a 3D object(comprised of a nickel alloy), including an exterior surface 5001 of theobject. The object in FIG. 50 includes a skin 5004 having (e.g.,substantially) aligned melt pools (e.g., 5080) and a core 5002 havingmelt pools (e.g., 5007).

In some cases, the microstructure features are grains. The grains maycomprise crystal structures that form during the hardening (e.g.,cooling) of the material of the 3D object. The grains may have anorientation with respect to a (e.g., average) layering plane, directionof build (e.g., layerwise deposition), and/or an exterior surface of the3D object. The grains may have an orientation with respect to anexternal surface of the 3D object. The grains may have an orientationwith respect to a center of a melt pool, an edge of a melt pool, or anaxis in a (e.g., central) portion of a melt pool. FIG. 52A shows anexample vertical section view of a portion of a 3D object, including anexterior surface 5201 of the object, and showing a grain structure ofthe object. The 3D object can include grains (e.g., 5208 or 5209) thatare oriented with respect to an alignment line (e.g., 5205). Thealignment line may be part of an alignment plane. In some embodiments,the alignment line is (e.g., substantially) orthogonal to the (e.g.,average) layering plane. In some embodiments, the alignment line is(e.g., substantially) orthogonal to the (e.g., average) cap (FIG. 14,1430) of the melt pool (e.g., FIG. 14, 1420). In some embodiments, thealignment line is (e.g., substantially) parallel to (i) a direction oflayerwise deposition and/or growth of the 3D object, and/or (ii) atleast a portion of the exterior surface (e.g., 5201) of the object. Insome embodiments, the alignment line follows a surface of the 3D objectadjacent to the melt pool. The alignment line may be a rotationalsymmetry axis. Without wishing to be bound to theory, the alignment linemay signify convergence of epitaxial growth of the grains towards aportion of the melt pool that (e.g., fully) hardened last, or thatremained hottest the longest. The alignment line may signify convergenceof epitaxial growth of the grains towards the center of the melt pool.The grains may grow epitaxially upon hardening of the melt pool. Forexample, the grains may grow towards the interior and/or the cap (e.g.,top) of the melt pool. During the hardening process of the melt pool, anedge (e.g., surface) of the melt pool can harden before its center,followed by (e.g., gradual) hardening of the center of the melt pool.During the hardening process of the melt pool, grains may form initiallyat an edge (e.g., surface) of the melt pool and propagate towards thecenter of the melt pool. The direction of grain propagation, their type,makeup, coherence length, and repeating units, may serve as anindication to the process forming the melt pool. The process may includea relation between temperature at various portions of the melt pool(e.g., exterior, and/or interior) over the hardening time of the meltpool. The grain may comprise a crystal. In some embodiments, theoriented grains are within a skin portion (e.g., 5204), which may be(e.g., chemically (e.g., metallically)) bound to a rigid structure suchas a core e.g., 5202). A portion of the 3D object associated with andforming the skin and a portion of the 3D object associated with andforming the core, may be separated by a border (e.g., 5203) thatindicates a change in grain structures between a process forming theskin and a process forming the core. In some embodiments, grains (e.g.,5208 or 5209) of one process (e.g., forming the skin) may have elongatedshapes as compared to another process (e.g., forming the core). Grainsindicative of a process (e.g., for forming the skin) may converge (e.g.,tend to meet in a point or line, e.g., along the direction of theobject's growth). The grains may converge at a central region (e.g.,middle) of the melt pool forming the portion (e.g., forming the skin).The grains may converge at the features alignment line (e.g., 5205). Thefeatures alignment line may be parallel to the direction of objectgrowth, and/or gravitational field vector. The features alignment linemay be perpendicular to the target surface, platform, and/or exposedsurface of a material bed that may be used in forming the 3D object. Theconverging grains may converge at a non-zero angle (e.g., about 10degrees, 15 degrees, 20 degrees, 25 degrees, 30 degrees, 35 degrees, 40degrees, 45 degrees or 50 degrees) relative to the features alignmentline. The converging grains (e.g., a vertical cross section thereof) mayhave a V-shape (e.g., chevron shape). An apex of the, v-shapedconverging grains may be pointed in a direction that is in accordancewith ((e.g., substantially) parallel to) the build direction (e.g., FIG.52, arrow labeled “Z”), which may also be referred to as a stackingvector. The build direction (stacking vector) can indicate a directionin which the layers of hardened material were bonded together (e.g.,printed). The portion (e.g., skin) may include multiple converginggrains (e.g., at least 2, 3, 4, 5, 6, 7, 8, 9 or 10). Grains (e.g., 5208or 5209) of the portion may be (e.g., on average) longer than grains(e.g., 5206) of another portion build by a different process (e.g., thecore, e.g., formed using hatching). In some embodiments, the grains ofthe portion (e.g., skin) have (e.g., average) lengths that are at leastabout 1.2, 1.5, 2, 3, 4, 5 or 6 times the (e.g., average) lengths ofgrains of the other portion (e.g., core). One portion may be formedusing a different process than the other (e.g., tiling vs. hatching.e.g., HARMP vs. PMX). In some embodiments, the grains of the portion(e.g., skin) have (e.g., average) lengths of at least about 300micrometers (μm), 320 μm, 330 μm, 340 μm, 350 μm or 400 μm. In someembodiments, the grains of the other portion (e.g., rigid structure orcore) have (e.g., average) lengths of at most about 50 μm, 60 μm, 70 μm,80 μm, 90 μm, 100 μm, 150 μm, 200 μm or 250 μm. In some embodiments, theone and/or other portion has pores. FIG. 52B shows an example verticalsection view of a portion of an object, showing a grain structure of theobject. In some embodiments, the skin (e.g., 5224) includes pores (e.g.,5226). The pores may be within a central region of the skin. The poresmay or may not be visible from an exterior surface (e.g., 5211) of theobject. The pores may be (e.g., substantially) spherical in shape. Thedensity of pores may be indicative of the type of process that is usedto form the portion. An (e.g., abrupt) variation in the density of poresmay be indictive of a transition from one process to another. Forexample, the skin may have a greater number of pores than the rigidportion (e.g., core. e.g., 5222). For example, one process may havepores and the other may not have pores. In some embodiments, the skinhas (e,g, substantially) no pores. In some embodiments, the core has(e.g., substantially) no pores.

The build direction (stacking vector (e.g., “Z”)) may be identified byany of number of features, such as growth direction of microstructures(e.g., tiles, melt pools, grains (e.g., crystals, e.g., dendrites)), thelocation of auxiliary support and/or support marks, surface roughnessvariations of the 3D object, energy beam path patterns (e.g., hatchpatterns) and/or tessellations, indicative of growth direction. Forexample, a melt pool may have a curved bottom portion (e.g., FIG. 50,5003 or 5007) indicative of the build direction (stacking vector). Forinstance, the curved bottom portion of a melt pool may be curved awayfrom (convex to) the build platform during printing and curved toward(concave to) the stacking direction. In some embodiments, the energybeam path patterns (e.g., hatch patterns) and/or tessellations may be ona top surface of the object relative to the platform during printing.

In some embodiments, the microstructures are indictive of a rate ofcooling, hardening and/or crystallization. In some embodiments, themicrostructures are indictive of faster or slower cooling, hardeningand/or crystallization rates. In some cases, the microstructure featuresare dendrites, which are branched crystal structures. The crystalstructures may be formed during the cooling and/or hardening of thematerial while forming the 3D object. In some cases, the microstructures(e.g., dendrites) are in the form of elongated structures. FIGS. 53A and53B show example section views of different portions of an example 3Dobject. FIG. 53A shows an example of crystal (e.g., dendritic) structureof a skin of the 3D object. FIG. 53B shows an example of crystal (e.g.,dendritic) structure of a core (e.g., rigid structure) of the 3D object.Crystals (e.g., dendrites) (e.g., 5302 or 5322) of one within the objectcan have elongated shapes. The microstructures may be separated byinter-microstructure regions. For example, dendrites can be separated byinterdendritic regions (e.g., light colored lines in FIGS. 53A or 53B).The inter-microstructure region e.g., interdendritic regions) maycorrespond to different phases of material than the phase of materialwithin the microstructure (e.g., of the crystal (e.g., dendrite)). Forexample, the inter-microstructure region may include higher or lowerconcentrations of certain elements as part of a (e.g., metal) alloy(e.g., molybdenum, titanium, nickel, aluminum, and/or niobium). In someembodiments the microstructure of a slower hardening region is (onaverage) different from microstructures of a faster hardening region ofthe 3D object. Different may be in size, material type, microstructureshape (e.g., globular or elongated), crystal structure, alignment (e.g.,direction), and/or coherence length. In some embodiments, themicrostructures of the skin are more organized than the microstructuresof the core. More organized may comprise more aligned, form a crystalwith larger coherence length, form a crystal with more repeating units,or form larger repeating units. Larger may comprise longer or wider. Insome embodiments, the grains(e.g., 5302 dendrites) of the skin are moreorganized (e.g., aligned) than the grains (e.g., 5322) of the core. Forexample, in some cases the grains (e.g., at least 2, 5, 10, 20, 50 or100 grains) of the skin are (e.g., substantially) aligned with respectto an alignment line (e.g., build line z). Aligned can be at an angle ofmost about 45 degrees, 40 degrees, 35 degrees, 30 degrees, 25 degrees,20 degrees, 15 degrees, 10 degrees or 5 degrees with respect to thealignment line (e.g., direction of build “Z”). In some embodiments, thewidths of the microstructures of one object portion are greater than thewidths of the microstructures of another object portion. In someembodiments, the widths of the crystals of one structure are greaterthan the widths of the crystals of one or more other structures. Forexample, the widths of the crystals (e.g., dendrites) can be determinedby measuring distances between the crystals interdendritic regions). Insome embodiments, a width of a crystal (e.g., dendrite) (or an averagewidth of a portion of crystals (e.g., dendrites)) of a first portion(e.g., skin) is/are at least about 1 micrometer (μm), 1.5 μm, 2 μm, 2.5or 3 μm. In some embodiments, a width of a crystal (e.g., dendrite) (oran average width of a portion of crystals (e.g., dendrites)) of a secondportion (e.g., core) is/are at most about 0.5 micrometers (μm), 0.7 μm,1 μm, 1.2 μm or 1.5 μm. In some embodiments, a width of a crystal (e.g.,dendrite) (or an average width of a portion of crystals (e.g.,dendrites)) of the first portion (e.g., skin) is/are at least about150%, 175%, 200% or 250% wider than a width of a crystal (e.g.,dendrite) (or an average width of a portion of crystals (e.g.,dendrites)) of the second portion (e.g., core). The crystal size (e.g.,dendrite length and/or width) can be associated with a solidification(hardening) rate of the material. In some embodiments, the size (e.g.,width) of a crystal (e.g., dendrite) (or an average size of a portion ofcrystals (e.g., dendrites)) of the first portion (e.g, skin) areassociated with a slower solidification (hardening) rate compared to asize (e.g., width) of a crystal (e.g., dendrite) (or an average width ofa portion of crystals (e.g., dendrites)) of the second portion (e.g.,core).

FIGS. 60A and 60B show example vertical cross-section views (atdifferent magnifications) of a portion of a 3D object (comprised of atitanium alloy). The skin (e.g., FIG. 60A, 6002; or FIG. 60B, 6022) canhave a different microstructure than that of an interior portion (core)(e.g., FIG. 60A, 6004; or FIG. 60B, 6024). In some embodiments, themicrostructure of the skin is indicative of a slower or fastersolidification (hardening) rate than that of the interior portion(core). For example, the skin can have grains (e.g., crystals) (e.g.,FIG. 60A, 6003; or FIG. 60B, 6023) that are oriented with respect to analignment line (e.g., FIG. 60B, 6028). The alignment line may be (e.g.,substantially) parallel to an exterior surface (e.g., FIG. 60A, 6001; orFIG. 60B, 6021) of the object and/or a stacking vector (e.g., “Z”)indicating a build direction of the multiple layers of material. In someembodiments, the microstructure features (e.g., grains (e.g., crystals))of the skin may be oriented at a non-perpendicular angle (e.g., about 0degrees, 5 degrees, 10 degrees, 15 degrees, 20 degrees, 25 degrees, 30degrees, 35 degrees, 40 degrees, 45 degrees or 50 degrees) relative tothe alignment line. The microstructure features (e.g., grains (e.g.,crystals)) (e.g., FIG. 60A, 6005; or FIG. 60B, 6025) of the interiorportion (core) can be oriented in a (e.g., substantially) randomarrangement. At least a portion (e.g., one or more) of themicrostructure features (e.g., grains (e.g., crystals)) of the core maybe oriented (e.g., substantially) perpendicular to the alignment line.In some embodiments, the skin portion has a microstructure feature e.g.,grain (e.g., crystal)) having an average FLS of a portion ofmicrostructure features (e.g., grains (e.g., crystals)) of at leastabout 50 micrometers (μm), 100 μm, 150 μm, 200 μm, 250 μm, 300 μm, 400μm, 500 μm or 600 μm. In some embodiments, the interior portion (core)has a microstiucture feature having a FLS of at most about 50micrometers (μm), 60 μm, 70 μm, 80 μm, 90 μm, 100 μm, 150 μm or 200 μm.The FLS can comprise a length a width. In some embodiments, a skinportion includes a microstructure feature having a FLS that is at leastabout 150%, 200%, 300%, 400%, 500%, 600% or 700% of a microstructurefeature of an inner portion (core).

In some embodiments, the overhang portion (e.g., having a shallow orsteep angle relative to the layering plane) of an object has adistinctive microstructure. FIGS. 54A and 54B show example dendriticstructures of an overhang portion (e.g., at a steep angle) of a 3Dobject forming using a MTO operation. FIG. 54A shows an exampledendritic structure of the overhang after a first transformation process(e.g., using a hatching energy beam). FIG. 54B shows an exampledendritic structure of the overhang after a second transformationprocess using a HARMP energy beam). FIG. 54C shows an example dendriticstructure of a core portion of a 3D object (as a comparison to FIGS. 54Aand 54B). The second transformation process may alter the microstructureof the re-transformed portion. The first transformation process (e.g.,FIG. 54A) can result in forming a crystal (e.g., dendrite) having awidth (or an average width of a portion of crystals (e.g., dendrites))of at least about 1.5 μm, 2 μm, 2.5 μm, 3 μm, 3.5 μm, 4 μm, 4.5 μm, 5 μmor 5.5 μm. The second transformation process (e.g., FIG. 54B) can resultin forming a crystal (e.g., dendrite) having a width (or an averagewidth of a portion of crystals (e.g., dendrites)) of at least about 0.8μm, 1 μm, 1.3 μm, 1.5 μm, 1.8 μm, 2 μm, 2.3 μm, 2.5 μm or 2.8 μm. Insome embodiments, the second transformation process can result in theoverhang having a crystal (e.g., dendrite) width (or an average width ofa portion of crystals (e.g., dendrites)) that is at least about 35%,40%, 45%, 50%, 55% or 60% of a crystal (e.g., dendrite) width (or anaverage width of a portion of crystals (e.g., dendrites)) of theoverhang after the first transformation process. The secondtransformation process can result in the overhang having a crystal (e.g,dendrite) with a width (or an average width of a portion of crystals(e.g, dendrites)) that is at least about 120%, 150%, 200%, 250%, 300% or350% of a crystal (e.g., dendrite) with a width (or an average width ofa portion of crystals (e.g., dendrites)) of a second. portion (e.g.,core (e.g., FIG. 54C)). In some embodiments, the second transformationprocess can result in the overhang having a microstructure (e,g, grain)FLS that is at least about 10%. 15% 20%. 25%, 35%, 40%, 45%, 50%, 55% or60% of a FIS of a respective microstructure (e.g., grain) of theoverhang after the first transformation process. The min may comprise acrystal or a metallurgical microstructure. The second transformationprocess can result in the overhang having a microstructure (e.g., grain)having a FLS that is at least about 110%, 120%, 150%, 200%, 250%, 300%or 350% of a (respective) microstructure of a second portion (e.g.,core). In some embodiments, a FLS of a microstructure (e.g., grain) ofthe overhang after the second transformation process is at least about120%, 150%, 200%, 300%, 400%, 500% or 600% greater than a FLS of amicrostructure (e.g., grain) of a second portion (e.g., core).

FIGS. 55A and 55B show example dendritic structures of different typesof overhang portions (e.g., at a shallow angles) of 3D objects. FIG. 55Ashows an example dendritic structure of a ledge type overhang formedusing a hatching energy beam followed by a tiling energy beam. FIG. 55Bshows an example dendritic structure of a ceiling type of overhang usinga hatching energy beam followed by a tiling energy beam. FIG. 55C showsan example dendritic structure of a core portion of a 3D object (as acomparison to FIGS. 55A and 55B). The hatching and tiling energy beamoperation (e.g., FIG. 55A) can result in a ledge type overhang with acrystal (e.g., dendrite) having a width (or an average width of aportion of crystals (e.g., dendrites)) of at least about 2.5 μm, 3 μm,3.5 μm, 4 μm, 4.5 μm, 5 μm or 5.5 μm. The hatching and tiling energybeam (e.g., FIG. 55B) can result in a ceiling type overhang with acrystal (e.g., dendrite) having a width (or an average width of aportion of crystals (e.g., dendrites)) of at least about 3 μm, 3.5 μm, 4μm, 4.5 μm, 5 μm, 5.5 μm, 6 μm, 5 μm or 7 μm. In some embodiments, theledge type overhang (e.g., FIG. 55A) or a ceiling type overhang (e.g.,FIG. 55B) can have a crystal (e.g., dendrite) width (or an average widthof a portion of crystals (e.g., dendrites)) that is at least about 200%,300%, 400%, 500%, or 600% of a crystal (e.g., dendrite) width (or anaverage width of a portion of crystals (e.g., dendrites)) of anotherportion of the object e.g., core (e.g., FIG. 55C)). In some embodiments,the second transformation process can result in the overhang having amicrostructure (e.g., grain) having a FLS that is at least about 10%,15% 20%, 25%, 35%, 40%, 45%, 50%, 55% or 60% of a (respective) FLS of amicrostructure of the overhang after the first transformation process.The second transformation process can result in the overhang having acrystal. (e.g., dendrite) with a length (or an average length of aportion of crystals (e.g., dendrites)) that is at least about 110%,120%, 150%, 200%, 250%, 300% or 350% of a crystal g dendrite) with alength (or an average width of a portion of crystals (e.g., dendrites))of a second portion (e.g., core). In some embodiments, crystals (e.g.,dendrites) a ceiling type overhang (e.g., FIG. 55B) can have lesselongated shapes (e.g., having more equal lengths as widths (e.g.,cellular)) compared to crystals (e.g., dendrites) of a ledge typeoverhang (e.g., FIG. 55A). The less elongated shape may be at leastpartially attributed to a (e.g., substantially) non-epitaxial growth.For example, a portion of the ceiling may be grown on a pre-transformedmaterial (e.g., powder). A (e.g., substantially) non-epitaxial growthmay be associated with crystals (e.g., dendrites) growing with little orno thermal gradient from an already solidified material (e.g., rigidportion).

In some embodiments, at least a portion of the 3D object is formed in aprocess comprising forming a porous matrix (e.g., PMX). In some cases,an overhang is formed comprising forming a porous matrix. The overhangcan be thickened by using a porous matrix. Subsequent to its formation,the porous matrix may be densified using any methods described herein(e.g., tiling, hatching and/or HARMP operation). FIG. 56A shows anexample dendritic structure of an overhang of a 3D object formed using aporous matrix sandwich structure (e.g., FIG. 40A) followed bydensification using a tiling energy beam. FIG. 56B shows an exampledendritic structure of a core portion of a 3D object (as a comparison toFIG. 56A). Forming a porous matrix (e.g., sandwich) structure followedby densification using a tiling energy beam can result in an overhangwith a microstructure (e.g., cmvstal, e.g., dendrite) having a width (oran average width of a portion of crystals (e.g., dendrites)) of at leastabout 2 μm, 3 μm, 4 μm or 5 μm. In some embodiments, the overhang canhave a microstructure having a FLS that is at least about 200%, 300%,400% or 500% of a FLS of a (respective) microstructure of anotherportion of the object (e.g., core (e.g., FIG. 56C)).

In some embodiments, the overhang portion of an object has a distinctivemelt pool structure and/or surface features, FIGS. 57A-57D show examplesof various views of an overhang portion of an. object formed using ahatching energy beam followed by tiling energy beam. FIG. 57A shows anexample top surface 5700 and side surface 5701 of an overhang. FIG. 57Bshows an example bottom surface (e.g., bottom skin) of an overhang. Theside surface (e.g., 5701) of the overhang may be formed using differenttypes of energy beams and/or process (e.g., alternating hatching andtiling) than the top surface 5700. In the example shown in FIG. 57A, theside surface 5701 is part of a first transformation to form the layer ofhardened material (using a first process), and the surface 5700 is partof a second transformation to form the layer of hardened material (usinga second process different than the first process). The second processmay comprise tiling. FIGS. 57C and 57D show example section views of theoverhang, with FIG. 57D showing an example melt pool structure. Asurface (e.g., top surface of FIG. 57A) of the object may have (e.g.,siibstantially) circular shaped tiles formed from a tiling energy beam.In some cases, adjacent tiles overlap with each other. In someembodiments, the top surface of an overhang is subsequently covered by arigid structure and/or structure formed using a PMX process. A skin(e.g., bottom skin (e.g., FIG. 57B)) of the overhang may have a surfaceroughness at or below a prescribed value (e.g., of at most about 50 μm,40 μm, 30 μm, 20 μm, 10 μm, or 5 μm). The skin (e.g., bottom skin) ofthe object shown in the example of FIG. 57A, is measured to have an areasurface roughness (Sa) of about 48 μm. The tiling energy beam may formmelt pools (e.g., 5702) that are (e.g., substantially) aligned with analignment line (e.g., 5704) that is at an angle no greater than about 15degrees, 10 degrees or 5 degrees with respect to a (e.g., average)layering plane of the object.

FIGS. 58A-58D show examples of various views of an overhang portion ofan object formed using an MTO operation (e.g., using a hatching energybeam followed by HARMP operation). FIG. 58A shows a top surface of theoverhang. FIG. 58B shows an example surface (e.g., bottom skin) of theoverhang. FIGS. 58C and 58D show example section views of the overhang,with FIG. 58D showing an example melt pool structure. A surface (e.g.,top surface of FIG. 58A) of the object may have hatches formed from ahatching energy beam. In some cases, the (linear progression of the)hatches may appear linear in shape, e.g., at the surface. In someembodiments, the top surface of an overhang is subsequently covered by arigid portion and/or a portion formed using a PMX process. A skin (e.g.,bottom skin) of the object in FIG. 58A is measured to have an areasurface roughness (Sa) of about 31 μm. A second transformation operation(e.g., HARMP, hatching or tiling) may form high aspect ratio melt pools(e.g., 5802) having bottom portions (e.g., 5804) that are (e.g.,substantially) aligned with a direction of the transforming energy beamand top portions (e.g., 5804) having more diffuse melt pools structure.In some embodiments, the bottom portions of melt pools are (e.g.,substantially) parallel with each other. In some embodiments, the bottomportions of melt pools are arranged in an angle of at most about 45°,40°, 35°, 30°, 20°, 10°, or 5° with respect to a (e.g., average)layering plane of the object.

In some embodiments, a second transformation operation (e.g., HARMP,hatching, or tiling) is used to alter (e.g., reduce) the porosity of(e.g., in) an object. FIGS. 59A and 59B show example section views of anoverhang portion of an object before and after a HARMP operation as thesecond transformation. FIG. 59A shows an example overhang formed using atiling energy beam. In some embodiments, the tiling energy beam causesthe overhang to have a porosity (v/v, or area/area porosity, e.g., of across-section plane of maximum porosity) of at most about 0.5% 1%, 2%,3%, 5%, 10% or 15%. The object in FIG. 59A has pores (e.g., 5901) andhas as a measured porosity of about 8.24%. FIG. 59B shows an exampleoverhang after a subsequent HARMP operation. A second transformationoperation (e.g., HARMP, hatching or tiling) may cause the overhang tohave a porosity (v/v, or area/area porosity, e.g., of a cross-sectionplane of maximum porosity) of at most about 0.01%, 0.02%, 0.03%, 0.04%,0.05%, 0.06%, 0.07%, 0.08%, 0.09%, 0.1% or 0.5%. The object in FIG. 59Bhas as a measured porosity of about 0.04%. The reduction in porosity maybe by at least one order of magnitude.

At times, the controller comprises a processing unit. The processingunit may be central. The processing unit may comprise a centralprocessing unit (herein “CPU”). The controllers or control mechanisms(e.g., comprising a computer system.) may be programmed to implementmethods of the disclosure. The controller may control at least onecomponent of the systems and/or apparatuses disclosed herein. FIG. 13 isa schematic example of a computer system 1300 that is programmed orotherwise configured to facilitate the formation of a 3D objectaccording to the methods provided herein. The computer system 900 cancontrol (e.g., direct and/or regulate) various features of printingmethods, apparatuses and systems of the present disclosure, such as, forexample, regulating force, translation, heating, cooling and/ormaintaining the temperature of a material bed, process parameters (e.g,chamber pressure), scanning rate (e.g., of the energy beam and/or theplatform), scanning route of the energy source, position and/ortemperature of the cooling member(s), application of the amount ofenergy emitted to a selected location, or any combination thereof. Thecomputer system 1300 can be part of, or be in communication with, aprinting system or apparatus, such as a 3D printing system or apparatusof the present disclosure. The computer may be coupled to one or moremechanisms disclosed herein, and/or any parts thereof. For example, thecomputer may be coupled to one or more sensors, valves, switches,motors, pumps, optical components, or any combination thereof.

In some embodiments, the computer system 1300 includes a processing unit1306 (also “processor,” “computer” and “computer processor” usedherein). The computer system may include memory or memory location 1302(e.g., random-access memory, read-only memory, flash memory), electronicstorage unit 1304 (e.g., hard disk), communication interface 1303 (e.g.,network adapter) for communicating with one or more other systems, andperipheral devices 1305, such as cache, other memory, data storageand/or electronic display adapters. The memory 1302, storage unit 1304,interface 1303, and peripheral devices 1305 are in communication withthe processing unit 1306 through a communication bus (solid lines), suchas a motherboard. The storage unit can be a data storage unit (or datarepository) for storing data. The computer system can be operativelycoupled to a computer network (“network”) 1301 with the aid of thecommunication interface. The network can be the Internet, an internetand/or extranet, or an intranet and/or extranet that is in communicationwith the Internet. In some cases, the network is a telecommunicationand/or data network. The network can include one or more computerservers, which can enable distributed computing, such as cloudcomputing. The network, in some cases with the aid of the computersystem, can implement a peer-to-peer network, which may enable devicescoupled to the computer system to behave as a client or a server.

The processing unit can execute a sequence of machine-readableinstructions, which can he embodied in a program or software. Theinstructions may be stored in a memory location, such as the memory1302. The instructions can he directed to the processing unit, which cansubsequently program or otherwise configure the processing unit toimplement methods of the present disclosure. Examples of operationsperformed by the processing unit can include fetch, decode, execute, andwrite back. The processing unit may interpret and/or executeinstructions. The processor may include a microprocessor, a dataprocessor, a central processing unit (CPU), a graphical processing unit(CPU), a system-on-chip (SOC), a co-processor, a network processor, anapplication specific integrated circuit (ASIC), an application specificinstruction-set processor (ASIPs), a controller, a programmable logicdevice (PLD), a chipset, a field programmable gate array (FPGA), or anycombination thereof. The processing unit can be part of a circuit, suchas an integrated circuit. One or more other components of the system 900can be included in the circuit.

The storage unit 1304 can store files, such as drivers, libraries andsaved programs. The storage unit can store user data (e.g., userpreferences and user programs). In some cases, the computer system caninclude one or more additional data storage units that are external tothe computer system, such as located on a remote server that is incommunication with the computer system through an intranet or theInternet.

The computer system can communicate with one or more remote computersystems through the network. For instance, the computer system cancommunicate with a remote computer system of a user (e.g., operator).Examples of remote computer systems include personal computers (e.g.,portable PC), slate or tablet. PC's (e.g., Apple® iPad, Samsung® GalaxyTab), telephones, Smart phones (e.g., Apple® iPhone, Android-enableddevice, Blackberry®), or personal digital assistants. The user canaccess the computer system via the network.

Methods as described herein can be implemented by way of machine (e.g.,computer processor) executable code stored on an electronic storagelocation of the computer system, such as, for example, on the memory1302 or electronic storage unit 1304. The machine executable ormachine-readable code can be provided in the form of software. Duringuse, the processor 1306 can execute the code. In some cases, the codecan be retrieved from the storage unit and stored on the memory forready access by the processor. In some situations, the electronicstorage unit can be precluded, and machine-executable instructions arestored on memory.

The code can be pre-compiled and configured for use with a machine havea processor adapted to execute the code, or can be compiled duringruntime. The code can be supplied in a programming language that can beselected to enable the code to execute in a pre -compiled or as-compiledfashion.

At times, the processing unit includes one or more cores. The computersystem may comprise a single core processor, multi core processor, or aplurality of processors for parallel processing. The processing unit maycomprise one or more central processing unit (CPU) and/or a graphicprocessing unit (GPU). The multiple cores may be disposed in a physicalunit (e.g., Central Processing Unit, or Graphic Processing Unit). Theprocessing unit may include one or more processing units. The physicalunit may be a single physical unit. The physical unit may be a die. Thephysical unit may comprise cache coherency circuitry. The multiple coresmay be disposed in close proximity. The physical unit may comprise anintegrated circuit chip. The integrated circuit chip may comprise one ormore transistors. The integrated circuit chip may comprise at leastabout 0.2 billion transistors (BT), 0.5 BT, 1 BT, 2 BT, 3 BT, 5 BT, 6BT, 7 BT, 8 BT, 9 BT, 10 BT, 15 BT, 20 BT, 25 BT, 30 BT, 40 BT, or 50BT. The integrated circuit chip may comprise at most about 7 BT, 8 BT, 9BT, 10 BT, 15 BT, 20 BT, 25 BT, 30 BT, 40 BT, 50 BT, 70 BT, or 100 BT.The integrated circuit chip may comprise any number of transistorsbetween the afore-mentioned numbers (e.g., from about 0.2 BT to about100 BT, from about 1 BT to about 8 BT, from about 8 BT to about 40 BT,or from about 40 BT to about 100 BT). The integrated circuit chip mayhave an area of at least about 50 mm², 60 mm², 70 mm², 80 mm², 90 mm²,100 mm², 200 mm², 300 mm², 400 mm², 500 mm², 600 mm², 700 mm², or 800mm². The integrated circuit chip may have an area of at most about 50mm², 60 mm², 70 mm ², 80 mm², 90 mm², 100 mm², 200 mm², 300 mm², 400mm², 500 mm², 600 mm², 700 mm², or 800 mm². The integrated circuit chipmay have an area of any value between the afore-mentioned values (e.g.,front about 50 mm² to about 800 mm², from about 50 mm² to about 500 mm²,or from about 500 mm² to about 800 mm²). The close proximity may allowsubstantial preservation of communication signals that travel betweenthe cores. The close proximity may diminish communication signaldegradation. A core as understood herein is a computing component havingindependent central processing capabilities. The computing system maycomprise a multiplicity of cores, which are disposed on a singlecomputing component. The multiplicity of cores may include two or moreindependent central processing units. The independent central processingunits may constitute a unit that read and execute program instructions.The independent central processing units may constitute parallelprocessing units. The parallel processing units may be cores and/ordigital signal processing slices (DSP slices). The multiplicity of corescan be parallel cores. The multiplicity of DSP slices can be parallelDSP slices. The multiplicity of cores and/or DSP slices can function inparallel. The multiplicity of cores may include at least about 2, 10,40, 100, 400, 1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000,10000, 11000, 12000, 13000, 14000 or 15000 cores. The multiplicity; ofcores may include at most about 1000, 2000, 3000, 4000, 5000, 6000,7000, 8000, 9000, 10000, 11000, 12000, 13000, 14000, 15000, 20000,30000, or 40000 cores. The multiplicity of cores may include cores ofany number between the afore-mentioned numbers (e.g., from about 2 toabout 40000, from about 2 to about 400, from about 400 to about 4000,from about 2000 to about 4000, from about 4000 to about 10000, fromabout 4000 to about 15000, or from about 15000 to about 40000 cores). Insome processors (e.g., FPGA) the cores may be equivalent to multipledigital signal processor (DSP) slices (e.g., slices). The plurality ofDSP slices may be equal to any of plurality core values mentionedherein. The processor may comprise low latency in data transfer (e.g.,from one core to another). Latency may refer to the time delay betweenthe cause and the effect of a physical change in the processor (e.g., asignal). Latency may refer to the time elapsed from the source (e.g.,first core) sending a packet to the destination (e.g., second core)receiving it (also referred as two-point latency). One-point latency mayrefer to the time elapsed from the source (e.g., first core) sending apacket (e.g., signal) to the destination (e.g., second core) receivingit, and the designation sending a packet back to the source (e.g., thepacket making a round trip). The latency may be sufficiently low toallow a high number of floating point operations per second (FLOPS). Thenumber of FLOPS may be at least about 1 Tera Flops (T-FLOPS), 2 T-FLOPS,3 T-FLOPS, 5 T-FLOPS, 6 T-FLOPS, 7 T-FLOPS, 8 T-FLOPS, 9 T-FLOPS, or 10T-FLOPS. The number of flops may be at most about 5 T-FLOPS, 6 T-FLOPS,7 T-FLOPS, 8 T-FLOPS, 9 T-FLOPS, 10 T-FLOPS, 20 T-FLOPS, 30 T-FLOPS, 50T-FLOPS, 100 T-FLOPS, 1 P-FLOPS, 2 P-FLOPS, 3 P-FLOPS, 4 P-FLOPS, 5P-FLOPS, 10 T-FLOPS, 50 P-FLOPS, 100 P-FLOPS, 1 EXA-FLOP, 2 EXA-FLOPS or10 EXA-FLOPS. The number of FLOPS may be any value between theafore-mentioned values (e.g., from about 0.1 T-FLOP to about 10EXA-FLOPS, from about 0.1 T-FLOPS to about 1 T-FLOPS, from about 1T-FLOPS to about 4 T-FLOPS, from about 4 T-FLOPS to about 10 T-FLOPS,from about 1 T-FLOPS to about 10 T-FLOPS, or from about 10 T-FLOPS toabout 30 T-FLOPS, from about 50 T-FLOPS to about 1 EXA-FLOP, or frontabout 0.1 T-FLOP to about 10 EXA-FLOPS). In some processors (e.g.,FPGA), the operations per second may be measured as (e.g., Giga)multiply-accumulate operations per second (e.g., MACs or GMACs). TheMACs value can be equal to any of the T-FLOPS values mentioned hereinmeasured as Tera-MACs (T-MACs) instead of T-FLOPS respectively. TheFLOPS can be measured according to a benchmark. The benchmark may be aHPC Challenge Benchmark. The benchmark may comprise mathematicaloperations (e.g., equation calculation such as linear equations),graphical operations (e.g., rendering), or encryption/decryptionbenchmark. The benchmark may comprise a High Performance UNPACK, matrixmultiplication (e.g., DGEMM) sustained memory bandwidth to/from memoity(e.g. STREAM), array transposing rate measurement (e.g., PTRANS).

Random-access, rate of Fast Fourier Transform (e.g., on a largeone-dimensional vector using the generalized Cooley-Tukey algorithm), orCommunication Bandwidth and Latency (e.g., MPI-centric performancemeasurements based on the effective bandwidth/latency benchmark).LINPACK may refer to a software library for performing numerical linearalgebra on a digital computer. DGEMM may refer to double precisiongeneral matrix multiplication. STREAM benchmark may refer to a syntheticbenchmark designed to measure sustainable memory bandwidth (in MB/s) anda corresponding computation rate for four simple vector kernels (Copy,Scale, Add and Triad). PTRANS benchmark may refer to a rate measurementat which the system can transpose a large array (global). MPI refers toMessage Passing Interface.

At times, the computer system includes hyper-threading technology. Thecomputer system may include a chip processor with integrated transform,lighting, triangle setup, triangle clipping, rendering engine, or anycombination thereof. The rendering engine may be capable of processingat least about 10 million polygons per second. The rendering engines maybe capable of processing at least about 10 million calculations persecond. As an example, the GPU may include a CPU by NVidia, ATITechnologies, S3 Graphics, Advanced Micro Devices AMD), or Matrox. Theprocessing unit may be able to process algorithms comprising a matrix ora vector. The core may comprise a complex instruction set computing core(CISC), or reduced instruction set computing (RISC).

At times, the computer system includes an electronic chip that isreprogrammable (e.g., field programmable gate array (FPGA)). Forexample, the FPGA may comprise Tabula, Altera, or Xilinx FPGA. Theelectronic chips may comprise one or more programmable logic blocks(e.g., an array). The logic blocks may compute combinational functions,logic gates, or any combination thereof. The computer system may includecustom hardware. The custom hard wale may comprise an algorithm.

At times, the computer system includes configurable computing, partiallyreconfigurable computing, reconfigurable computing, or any combinationthereof. The computer system may include a FPGA. The computer system mayinclude an integrated circuit that performs the algorithm For example,the reconfigurable computing system may comprise FPGA, CPU, GPU, ormulti-core microprocessors. The reconfigurable computing system maycomprise a High-Performance Reconfigurable Computing architecture(HPRC). The partially reconfigurable computing may include module-basedpartial reconfiguration, or difference-based partial reconfiguration.

At times, the computing system includes an integrated circuit thatperforms the algorithm (e.g., control algorithm). The physical unit(e.g., the cache coherency circuitry within) may have a clock time of atleast about 0.1 Gigabits per second (Gbit/s), 0.5 Gbit/s, 1 Gbit/s, 2Gbit/s, 5 Gbit/s, 6 Gbit/s, 7 Gbit/s, 8 Gbit/s, 9 Gbit/s, 10 Gbit/s, or50 Gbit/s. The physical unit may have a clock time of any value betweenthe afore-mentioned values (e.g., from about 0.1 Gbit/s to about 50Gbit/s, or from about 5 Gbit/s to about 10 Gbit/s). The physical unitmay produce the algorithm output in at most about 0.1 microsecond (μs),1 μs, 10 μs, 100 μs, or 1 millisecond (ms). The physical unit mayproduce the algorithm output in any time between the afore-mentionedtimes (e.g., from about 0.1 to about 1 ms, from about 0.1 μs, to about100 μs, or from about 0.1 μs to about 10 μs).

In some instances, the controller uses calculations, real timemeasurements, or any combination thereof to regulate the energy beam(s).The sensor (e.g., temperature and/or positional sensor) may provide asignal (e.g., input for the controller and/or processor) at a rate of atleast about 0.1 KHz, 1 KHz, 10 KHz, 100 KHz, 1000 KHz, or 10000 KHz).The sensor may provide a signal at a rate between any of theabove-mentioned rates (e.g., from about 0.1 KHz to about 10000 KHz, fromabout 0.1 KHz to about 1000 KHz, or from about 1000 KHz to about 10000KHz). The memory bandwidth of the processing unit may be at least about1 gigabytes per second (Gbytes/s), 10 Gbytes/s, 100 Gbytes/s, 200Gbytes/s, 300 Gbytes/s, 400 Gbytes/s, 500 Gbytes/s, 600 Gbytes/s, 700Gbytes/s, 800 Gbytes/s, 900 Gbytes/s, or 1000 Gbytes/s. The memorybandwidth of the processing unit may be at most about 1 gigabytes persecond (Gbytes/s), 10 Gbytes/s, 100 Gbytes/s, 200 Gbytes/s, 300Gbytes/s, 400 Gbytes/s, 500 Gbytes/s, 600 Gbytes/s, 700 Gbytes/s, 800Gbytes/s, 900 Gbytes/s, or 1000 Gbytes/s, The memory bandwidth of theprocessing unit may have any value between the afore-mentioned values(e.g., from about 1 Gbytes/s to about 1000 Gbytes/s, from about 100Gbytes/s to about 500 Gbytes/s, from about 500 Gbytes/s to about 1000Gbytes/s, or from about 200 Gbytes/s to about 400 Gbytes/s). The sensormeasurements may be real-time measurements. The real-time measurementsmay be conducted during the 3D printing process. The real-timemeasurements may be in-situ measurements in the 3D printing systemand/or apparatus. The real-time measurements may be during the formationof the 3D object. In some instances, the processing unit may use thesignal obtained from the at least one sensor to provide a processingunit output, which output is provided by the processing system at aspeed of at most about 100 min, 50 min, 25 min, 15 min, 10 min, 5 min, 1min, 0.5 min (i.e., 30 sec). 15 sec, 10 sec, 5 sec, 1 sec, 0.5 sec, 0.25sec, 0.2 sec, 0.1 sec, 80 milliseconds (msec), 50 msec, 10 msec, 5 msec,or 1 msec. In some instances, the processing unit may use the signalobtained from the at least one sensor to provide a processing unitoutput, which output is provided at a speed of any value between theaforementioned values (e.g., from about 100 min to about 1 msec, fromabout 100 min to about 10 min, from about 10 min to about 1 min, fromabout 5 min to about 0.5 min, from about 30 sec to about 0.1 sec, orfrom about 0.1 sec to about 1 msec). The processing unit output maycomprise an evaluation of the temperature at a location, position at alocation (e.g., vertical and/or horizontal), or a map of locations. Thelocation may be on the target surface. The map may comprise atopological or temperature map.

At times, the processing unit uses the signal obtained from the at leastone sensor in an algorithm that is used in controlling the energy beam.The algorithm may comprise the path of the energy beam. In someinstances, the algorithm may be used to alter the path of the energybeam on the target surface. The path may deviate from a cross section ofa model corresponding to the requested 3D object. The processing unitmay use the output in an algorithm that is used in determining themanner in which a model of the requested 3D object may be sliced. Theprocessing unit may use the signal obtained from the at least one sensorin an algorithm that is used to configure one or more parameters and/orapparatuses relating to the 3D printing process. The parameters maycomprise a characteristic of the energy beam. The parameters maycomprise movement of the platform and/or material bed. The parametersmay comprise relative movement of the energy beam and the material bed.In some instances, the energy beam, the platform (e.g., material beddisposed on the platform), or both may translate. Alternatively, oradditionally, the controller may use historical data for the control.Alternatively, or additionally, the processing unit may use historicaldata in its one or more algorithms. The parameters may comprise theheight of the layer of pre-transformed material disposed in theenclosure and/or the gap by which the cooling element (e.g., heat sink)is separated from the target surface. The target surface may be theexposed layer of the material bed.

Aspects of the systems, apparatuses, and/or methods provided herein suchas the computer system, can be embodied in programming (e.g., using asoftware). Various aspects of the technology may be thought of as“product,” “object,” or “articles of manufacture” typically in the formof machine (or processor) executable code and/or associated data that iscarried on or embodied in a type of machine-readable medium.Machine-executable code can be stored on an electronic storage unit,such memory (e.g., read-only memory, random-access memory, flash memory)or a hard disk. The storage may comprise non-volatile storage media.“Storage” type media can include any or all the tangible memory of thecomputers, processors or the like, or associated modules thereof, suchas various semiconductor memories, tape drives, disk drives, externaldrives, and the like, winch may provide non-transitory storage at anytime for the software programming.

At times, the memory comprises a random-access memory (RAM), dynamicrandom access memory (DRAM), static random access memory (SRAM),synchronous dynamic random access memory (SDRAM), ferroelectric randomaccess memory (FRAM), read only memory (ROM), programmable read onlymemory (PROM), erasable programmable read only memory (EPROM),electrically erasable programmable read only mernoty (EEPROM), aflash:memory, or any combination thereof. The flash memory may comprisea negative-AND (NAND) or NOR logic gates. A NAND gate (negative-AND) maybe a logic gate which produces an output which is false only if all itsinputs are true. The output of the NAND gate may be complement to thatof the AND gate. The storage may include a hard disk (e.g., a magneticdisk, an optical disk, a magneto-optic disk, a solid-state disk, etc.),a compact disc (CD), a digital versatile disc (DVD), a floppy disk, acartridge, a magnetic tape, and/or another type of computer-readablemedium, along with a corresponding drive.

All or portions of the software may at times be communicated through theInternet or various other telecommunication networks. Suchcommunications, for example, may enable loading of the software from onecomputer or processor into another, for example, from a managementserver or host computer into the computer platform of an applicationserver. Thus, another type of media that may bear the software elementsincludes optical, electrical, and electromagnetic waves, such as usedacross physical interfaces between local devices, through wired andoptical landline networks and over various air-links The physicalelements that carry such waves, such as wired or wireless links, opticallinks, or the like, also may be considered as media bearing thesoftware. As used herein, unless restricted to non-transitory, tangible“storage” media, terms such as computer or machine “readable medium”refer to any medium that participates in providing instructions to aprocessor for execution.

Hence, a machine-readable medium, such as computer-executable code, maytake many forms, including but not limited to, a tangible storagemedium, a carrier wave medium, or physical transmission medium.Non-volatile storage media include, for example, optical or magneticdisks, such as any of the storage devices in any computer(s) or thelike, such as may be used to implement the databases. Volatile storagemedia can include dynamic memory, such as main memory of such a computerplatform. Tangible transmission media can include coaxial cables, wire(e.g., copper wire), and/or fiber optics, including the wires thatcomprise a bus within a computer system. Carrier-wave transmission mediamay take the form of electric or electromagnetic signals, or acoustic orlight waves such as those generated during radio frequency (RF) andinfrared (IR) data communications. Common forms of computer-readablemedia therefore include for example: a floppy disk, a flexible disk,hard disk, magnetic tape, any other magnetic medium, a CD-ROM, DVD orDVD-ROM, any other optical medium, punch cards paper tape, any otherphysical storage medium with patterns of holes, a RAM, a ROM, a PROM andEPROM, a FLASH-EPROM, any other memory chip or cartridge, a carrier wavetransporting data or instructions, cables or links transporting such acarrier wave, any other medium from which a computer may readprogramming code and/or data, or any combination thereof. The memoryand/or storage may comprise a storing device external to and/orremovable from device, such as a Universal Serial Bus (USB) memorystick, or/and a hard disk. Many of these forms of computer readablemedia may be involved in carrying one or more sequences of one or moreinstructions to a processor for execution.

The computer system can include or be in communication with anelectronic display that comprises a user interface (UI) for providing,for example, a model design or graphical representation of a 3D objectto be printed. Examples of UI's include, without limitation, a graphicaluser interface (GUI) and web-based user interface. The computer systemcan monitor and/or control various aspects of the 3D printing system.The control may be manual and/or programmed. The control may rely onfeedback mechanisms (e.g., from the one or more sensors). The controlmay rely on historical data. The feedback mechanism may bepre-programmed. The feedback mechanisms may rely on input from sensors(described herein) that are connected to the control unit (i.e., controlsystem or control mechanism e.g., computer) and/or processing unit. Thecomputer system may store historical data concerning various aspects ofthe operation of the 3D printing system. The historical data may beretrieved at predetermined times and/or at a whim. The historical datamay be accessed by an operator and/or by a user. The historical, sensor,and/or operative data may be provided in an output unit such as adisplay unit. The output unit (e.g., monitor) may output variousparameters of the 3D printing system (as described herein) in real timeor in a delayed time. The output unit may output the current 3D printedobject, the ordered 3D printed object, or both. The output unit mayoutput the printing progress of the 3D printed object. The output unitmay output at least one of the total time, time remaining, and timeexpanded on printing the 3D object. The output unit may output (e.g.,display, voice, and/or print) the status of sensors, their leading,and/or time for their calibration or maintenance. The output unit mayoutput the type of material(s) used and various characteristics of thematerial(s) such as temperature and flowability of the pre-transformedmaterial. The output unit may output the amount of oxygen, water, andpressure in the printing chamber (i.e., the chamber where the 3D objectis being printed). The computer may generate a report comprising variousparameters of the 3D printing system, method, and or objects atpredetermined time(s), on a request (e.g., from an operator), and/or ata whim. The output unit may comprise a screen, printer, or speaker. Thecontrol system may provide a report. The report may comprise any itemsrecited as optionally output by the output unit.

At times, the system and/or apparatus described herein (e.g.,controller) and/or any of their components comprises an output and/or aninput device. The input device may comprise a keyboard, touch pad, ormicrophone. The output device may be a sensory output device. The outputdevice may include a visual, tactile, or audio device. The audio devicemay include a loudspeaker. The visual output device may include a screenand/or a printed hard copy (e.g., paper). The output device may includea printer. The input device may include a camera, a microphone, akeyboard, or a touch screen. The system and/or apparatus describedherein (e.g., controller) and/or any of their components may compriseBluetooth technology. The system and/or apparatus described herein(e.g., controller) and/or any of their components may comprise acommunication port. The communication port may be a serial port or aparallel port. The communication port may be a Universal Serial Bus port(i.e., USB). The system and/or apparatus described herein (e.g.,controller) and/or any of their components may comprise USB ports. TheUSB can be micro or mini USB. The USB port may relate to device classescomprising 00h, 01h, 02h, 03h, 05h, 06h, 07h, 08h, 09h, 0Ah, 0Bh, 0Dh,0Eh, 0Fh, 10h, 11h, DCh, E0h, EFh, FEh, or FFh. The system and/orapparatus described herein (e, g., controller) and/or any of theircomponents may comprise a plug and/or a socket (e.g., electrical, ACpower, DC power). The system and/or apparatus described herein (e.g.,controller) and/or any of their components may comprise an adapter(e.g., AC and/or DC power adapter). The system and/or apparatusdescribed herein (e.g., controller) and/or any of their components maycomprise a power connector. The power connector can be an electricalpower connector. The power connector may comprise a magnetically coupled(e.g., attached) power connector. The power connector can be a dockconnector. The connector can be a data and power connector. Theconnector may comprise pins. The connector may comprise at least 10, 15,18, 20, 22, 24, 26, 28, 30, 40, 42, 45, 50, 55, 80, or 100 pins.

At times, the systems, methods, and/or apparatuses disclosed hereincomprises receiving a request for a 3D object (e.g., from a customer).The request can include a model (e.g., CAD) of the requested 3D object.Alternatively, or additionally, a model of the requested 3D object maybe generated. The model may be used to generate 3D printinginstructions. The 3D printing instructions may exclude the 3D model. The3D printing instructions may be based on the 3D model. The 3D printinginstructions may take the 3D model into account. The 3D printinginstructions may be alternatively or additionally be based onsimulations. The 3D printing instructions may use the 3D model. The 3Dprinting instructions may comprise using an algorithm (e.g., embedded ina software) that considers the 3D model, simulations, historical data,sensor input, or any combination thereof. The processor may compute thealgorithm during the 3D printing process (e.g., in real-time), duringthe formation of the 3D object, prior to the 3D printing process, afterthe 3D printing process, or any combination thereof. The processor maycompute the algorithm in the interval between pulses of the energy beam,during the dwell time of the energy beam, before the energy beamtranslates to a new position, while the energy beam is not translating,while the energy beam does not irradiate the target surface, while theenergy beam irradiates the target surface, or any combination thereof.For example, the processor may compute the algorithm while the energybeam translates and does substantially not irradiate the exposedsurface. For example, the processor may compute the algorithm while theenergy beam does not translate and irradiates the exposed surface. Forexample, the processor may compute the algorithm while the energy beamdoes not substantially translate and does substantially not irradiatethe exposed surface. For example, the processor may compute thealgorithm while the energy beam does translate and irradiates theexposed surface. The translation of the energy beam may be translationalong an entire path or a portion thereof. The path may correspond to across section of the model of the 3D object. The translation of theenergy beam may be translation along at least one hatching within thepath. FIG. 3 shows examples of various paths. The direction of thearrow(s) in FIG. 3 represents the direction according to which aposition of the energy beam directed to the exposed surface of thematerial bed is altered with respect to the material bed. The variousvectors depicted in FIG. 3, 314 show an example of various hatchings.The respective movement of the energy beam with the material bed mayoscillate while traveling along the path. For example, the propagationof the energy beam along a path may be by small path deviations (e.g.,variations such as oscillations). FIG. 2 shows an example of a path 201.The sub path 202 is a magnification of a portion of the path 201 showingpath deviations (e.g., oscillations).

EXAMPLES

The following are illustrative and non-limiting examples of methods ofthe present disclosure.

Example 1

In a 28 cm by 28 cm by 30 cm container at ambient temperature andpressure, Inconel 718 powder of average particle size 35 μm is depositedin a container to form a powder bed. The container is disposed in anenclosure to separate the powder bed from the ambient environment. Theenclosure is purged with Argon gas for 30 minutes. A 500 W fiber laserbeam was used to melt a portion of the powder bed and generate twosubstantially identical 3D objects, each comprising an extended ledgethat was anchored on one of its side to the base using auxiliarysupports. The ledge in each of the two 3D objects had an angle (e.g., ofabout 25°) with respect to the base, in which the laser beam pathfollowed a path scheme resembling the one shown in the example of FIG.3, 314. The 3D objects were, fabricated by successive deposition oflayers of powder material having an average thickness of about 50 μm andmelting portions of each of the successively deposited layers using thelaser beam. The auxiliary supports were formed using the methodology offorming the rigid-portion (e.g., using hatches) as described herein. Theledge in the first 3D object was formed by generating successivepartially overlapping layers of hardened material using the STOmethodology. The ledge in the second 3D object was formed by (i)depositing a powder layer having a thickens of 50 μm, (ii) generating alayer of hardened material using the STO methodology in a firsttransformation operation, (iii) transforming the layer of hardenedmaterial using HARMP methodology in a second transformation operationand successively repeating steps (i) to (iii) to generating therequested 3D object. Images of the first 3D object in which the ledge isformed using STO methodology are shown: as a cross section in FIG. 34A,as a topological top view image in FIG. 35B, and as a horizontal X-rayimage in FIG. 35A. Images of the second 3D object in which each layerforming the ledge is formed using STO methodology followed by HARMPmethodology, are shown as: a cross section in FIG. 34B, as a topologicaltop view image in FIG. 35D, and as a horizontal X-ray image in FIG 35C.The optical images of FIGS. 34A and 34B were taken using a Epiphot 300microscope manufactured by Nikon Corporation. The X ray images of FIGS.35A and 35C were taken using a VERTEX X-ray system manufactured by VJElectronix. The 3D scan images of FIGS. 35B and 35D were taken using aKeyence VR-3200 manufactured by Keyence Corporation. The surfaceroughness measurements were performed using the Keyence VR-3200 (surfaceprofilometer),

Example 2

In a 28 cm by 28 cm by 30 cm container at ambient temperature andpressure, Inconel 718 powder of average particle size 35 μm is depositedin a container to form a powder bed. The container is disposed in anenclosure to separate the powder bed from the ambient environment. Theenclosure is purged with Argon gas for 30 minutes. A 500 W fiber laserbeam was used to melt a portion of the powder bed and form a skin(contour) of a 3D object. The contour was formed by transforming layersof powder material having an average thickness of about 50 μm using atiling methodology (type-2 energy beam), as described herein. Theinternal portions of the 3D object layers were formed using amethodology of forming the rigid-portion (e.g., using hatches) asdescribed herein. Images of 3D objects in which a skin (contour) isformed using contour methodology are shown in FIGS. 38A and 38B. Thesurface roughness of the 3D objects depicted in FIGS. 38A and 38B wasmeasured using the Keyence VR-3200 (surface profilometer), to have an Savalue of 3.5 micrometers. Similar conditions and methodologies were usedto form the 3D objects depicted in FIGS. 50, 52A, 52B, 53A and 53B. Anoptical image of the 3D object shown in FIG. 50 is taken using the NikonEpiphot 300 microscope. Scanning electron microscope (SEM) images of theobject shown in FIGS. 52A, 52B, 53A, 53B, 54C, 55C and 56B are takenusing a Nova™ NanoSEM 630 manufactured by FEI Company (subsidiary ofThenno Fisher Scientific).

Example 3

In a 300 mm diameter and 400 mm high container at ambient temperature,Inconel 718 powder of average particle size 35 rim is deposited in acontainer to form a powder bed. The container is disposed in anenclosure to separate the powder bed from the ambient environment. Theenclosure is purged with Argon gas. A 1000W fiber laser beam was used tomelt a portion of the powder bed and form an overhang of a 3D object atan angle with respect to the platform base. The overhang was formed bytransforming layers of powder material having an average thickness ofabout 50 μm using a MTO process as described herein. A firsttransformation operation was performed used a hatching methodology(type-1 energy beam). A SEM image of the 3D object after the firsttransformation operation is shown in FIG. 54A using the Nova™ NanoSEM630. A second transformation operation was performed using a HARMPmethodology to re-transform (e.g., remelt) at least a portion of thepreviously transformed material. An SEM image of the 3D object after theHARMP operation is shown in FIG. 54B using the Nova™ NanoSEM 630.Three-dimensional scan images (and surface roughness measurements) ofthe object after the HARMP operation shown in FIGS. 58A and 58B wereobtained using the Keyence VR-3200. Optical images of the object afterthe HARMP operation shown in FIGS. 58C and 58D were obtained using theNikon Epiphot 300 microscope. Similar conditions and methodologies areused to form 3D objects depicted in FIGS. 57A-57D and 59A-59B. The 3Dscan images of the object shown in FIGS. 57A and 57B, as well as surfaceroughness measurements, were obtained using the Keyence VR-3200. Opticalimages of the object shown in FIGS. 57C and 57D were taken using theNikon Epiphot 300 microscope. The X-ray image of the 3D object shown inFIG. 59A after a first transformation of an MTO operation is obtainedusing a XT V160 instrument manufactured by Nikon to determine porosity.An X-ray image of the 3D object shown in FIG. 59B after the secondtransformation of the MTO operation is using the Nikon XT V160 todetermine porosity.

Example 4

In a 300 mm diameter and 400 mm high container at ambient temperature,Inconel 718 powder of average particle size 35 μm is deposited in acontainer to form a powder bed. The container is disposed in anenclosure to separate the powder bed from the ambient environment. Theenclosure is purged with Argon gas. A 1000 W fiber laser beam was usedto melt a portion of the powder bed and form an overhang portion of a 3Dobject at an angle with respect to the platform base. The overhang wasformed by transforming layers of powder material having an averagethickness of about 50 μm. The transformation included the following; afirst layer of powder is transformed using a hatching methodology(type-1 energy beam) to a first transformed material: a second layer ofpowder is deposited on the first transformed material; the second layerof powder is transformed using a tiling methodology (type-2 energy beam)to a second transformed material. At least some of the first transformedmaterial may be re-transformed (e.g., remelted) using the tilingmethodology. An SEM image of the overhang portion is shown in FIG. 55Ausing the Nova™ NanoSEM 630.

Example 5

In a 28 cm by 28 cm by 30 300 mm diameter and 400 mm high cm containerat ambient temperature, Inconel 718 powder of average particle size 35μm is deposited in a container to form a powder bed. The container isdisposed in an enclosure to separate the powder bed from the ambientenvironment. The enclosure is purged with Argon gas. A 1000 W fiberlaser beam was used to melt a portion of the powder bed and form aceiling type overhang of a 3D object at an angle with respect to theplatform base. The ceiling type overhang was formed by transforminglayers of powder material having an average thickness of about 50 μm.The transformation included using at least one hatching methodology(type-1 energy beam) and at least one a tiling methodology (type-2energy beam. At least some of the transformed material mayre-transformed (e.g., remelted) using the tiling anchor hatchingmethodologies. An SEM image of the ceiling overhang is shown in FIG. 55Busing the Nova™ NanoSEM 630.

Example 6

In a 300 mm diameter and 400 mm high container at ambient temperature,Inconel 718 powder of average particle size 35 μm is deposited in acontainer to form a powder bed. The container is disposed in anenclosure to separate the powder bed from the ambient environment. Theenclosure is purged with Argon gas. A 1000W fiber laser beam was used tomelt a portion of the powder bed and form an overhang of a 3D object atan angle with respect to the platform base. The overhang was formed bytransforming layers of powder material having an average thickness ofabout 50 μm. The transformation included forming a plurality of layersof porous matrix using a hatching methodology (type-1 energy beam),which are transformed (e.g., melted anchor re-melted) using a tilingmethodology (type-2 energy beam). An SEM image of the overhang is shownin FIG. 56A using the Nova™ NanoSEM 630.

Example 7

In a 300 mm diameter and 400 mm high container at ambient temperature,titanium alloy (Ti-6Al-4V) powder of average particle of about size 33μm is deposited in a container to form a powder bed. The container isdisposed in an enclosure to separate the powder bed from the ambientenvironment. The enclosure is purged with Argon gas. A 1000 W fiberlaser beam was used to melt a portion of the powder bed and form a skin(contour) of a 3D object. The contour was formed by transforming layersof powder material having an average thickness of about 50 μm using atiling methodology (type-2 energy beam), as described herein. Theinternal portions (core) of the 3D object layers were formed using amethodology of forming the rigid-portion (e.g., using hatches) asdescribed herein. Images of 3D objects in which a skin (contour) andinternal portion (core) are shown in FIGS. 60A and 60B taken using theNikon Epiphot 300 microscope.

While preferred embodiments of the present invention have been shown,and described herein, it will be obvious to those skilled in the artthat such embodiments are provided by way of example only. It is notintended that the invention be limited by the specific examples providedwithin the specification. While the invention has been described withreference to the aforementioned specification, the descriptions andillustrations of the embodiments herein are not meant to be construed ina limiting sense. Numerous variations, changes, and substitutions willnow occur to those skilled in the art without departing from theinvention. Furthermore, it shall be understood that all aspects of theinvention are not limited to the specific depictions, configurations, orrelative proportions set forth herein which depend upon a variety ofconditions and variables. It should be understood that variousalternatives to the embodiments of the invention described herein may beemployed in practicing the invention. It is therefore contemplated thatthe invention shall also cover any such alternatives, modifications,variations, or equivalents. It is intended that the following claimsdefine the scope of the invention and that methods and structures withinthe scope of these claims and their equivalents be covered thereby.

What is claimed is:
 1. A method of printing a three-dimensional object,comprising: (a) transforming a first pre-transformed material to a firsttransformed material to print one or more layers of hardened material aspart of the three-dimensional object that is printed layerwise, whichone or more layers define a layering plane indicative of a layerwiseprinting of the three-dimensional object; (b) transforming a secondpre-transformed material to a second transformed material to print atleast a portion of an overhang of the three-dimensional object, whereina vector normal to a surface at a point on an exterior surface of theoverhang that intersects (i) the layering plane or (ii) a plane parallelto the layering plane, forms an angle with respect to the layeringplane, which second transformed material comprises a porous matrix; and(c) using an energy beam to densify the second transformed material. 2.The method of claim 1, wherein the angle is at least about sixty degreesand most about ninety degrees with respect to (i) the layering planethat intersects the vector or to (ii) a plane parallel to the layeringplane that intersects the vector, wherein the vector is directed towardsthe second transformed material.
 3. The method of claim 1, wherein usingan energy beam to densify comprises altering a microstructure of thefirst transformed material to form the second transformed material. 4.The method of claim 1, wherein (c) comprises forming a high aspect ratiomelt pool, wherein a depth of the high aspect ratio melt pool is greaterthan a radius of an exposed surface of the high aspect ratio melt pool.5. The method of claim 1, wherein (c) comprises reducing an areapercentage porosity of the second transformed material by at least aboutone order of magnitude.
 6. The method of claim 1, wherein the secondtransformed material comprises a plurality of layers, wherein (c)comprises transforming at least a portion of each of the plurality oflayers.
 7. The method of claim 1, wherein the second transformedmaterial corresponds to at least a portion of a skin of thethree-dimensional object.
 8. The method of claim 7, wherein the skin isa bottom skin, and wherein the bottom skin has an area surface roughness(Sa) of at most about 20 micrometers.
 9. The method of claim 1, whereinthe porous matrix in (b) forms a bottom skin of the overhang.
 10. Themethod of claim 1, wherein densification in (c) comprises directing theenergy beam in accordance with a path along or parallel to an edge ofthe first transformed material.
 11. The method of claim 1, whereincomprises using a hatching energy beam and (c) comprises using a tilingenergy beam.
 12. The method of claim 11, wherein a spot size of thehatching energy beam is smaller than a spot size of the tiling energybeam.
 13. The method of claim 1, wherein the energy beam in (c) is athird energy beam, wherein the method further comprises using a firstenergy beam to transform the first pre-transformed material in (a),using a second energy beam to transform the second pre-transformedmaterial in (b), and wherein (i) the first energy beam, the secondenergy beam, and/or the third energy beam follow a hatching propagationscheme, wherein a hatching propagation scheme comprises transformingwhile translating along a path.
 14. The method of claim 1, wherein theenergy beam in (c) is a third energy beam, wherein the method furthercomprises using a first energy beam to transform the firstpre-transformed material in (a), using a second energy beam to transformthe second pre-transformed material in (b), and wherein (i) the firstenergy beam, the second energy beam, and/or the third energy beam followa tiling propagation scheme, wherein tiling propagation scheme comprises(1) transforming while being stationary or substantially stationaryfollowed by (II) propagating along a path to a second point withouttransforming and MD repeating (I) and (II) until reaching an end of thepath.
 15. An apparatus for printing a three-dimensional object,comprising one or more controllers that are individually or collectivelyprogrammed to: (a) direct transforming a first pre-transformed materialto a first transformed material to print one or more layers of hardenedmaterial as part of the three-dimensional object that is printedlayerwise,which one or more layers define a layering plane indicative ofa layerwise printing of the three-dimensional object; (b) directtransforming a second pre-transformed material to a second transformedmaterial to print at least a portion of an overhang, of thethree-dimensional object, wherein a vector normal a surface at a pointon an exterior surface of the overhang that intersects (i) the layeringplane or (ii) a plane parallel to the layering plane, forms an anglewith respect to the layering plane, which second transformed materialcomprises a porous matrix; and (c) direct an energy beam to densify thesecond transformed material.
 16. The apparatus of claim 15, wherein theenergy beam is a third energy beam, wherein direct transforming thefirst pre-transformed material in (a) is by directing a first energybeam to transform the first pre-transformed material, and wherein directtransforming the second pre-transformed material in (b) is by directinga second energy beam to transform the second pre-transformed material.17. The apparatus of claim 16, wherein the one or more controllerscontrols at least one characteristic of the first energy beam the secondenergy author the third energy beam at least partially based on datafrom one or more sensors.
 18. The apparatus of claim 17, wherein the oneor more sensors collect temperature, optical, or spectroscopic data. 19.The apparatus of claim 17, wherein the one or more sensors detectelectromagnetic radiation that is emitted and/or reflected from anexposed surface of one or more melt pools formed during transformationin (a), (b) and/or (c).
 20. The apparatus of claim 16, wherein the oneor more controllers is programmed to direct forming a high aspect ratiomelt pool during (c), wherein a depth of the high aspect ratio melt poolis greater than a width of the high aspect ratio melt pool.
 21. Theapparatus of claim 16, wherein the first transformed material comprisesan edge, wherein the one or more controllers is programmed to direct thesecond energy beam and/or the third energy beam in accordance with apath along the edge or to a path parallel to the edge.
 22. The apparatusof claim 16, wherein the one or more controllers is programmed to (i)direct the first energy beam, the second energy beam and/or the thirdenergy beam to propagate via hatching propagation scheme.
 23. Theapparatus of claim 22, wherein hatching comprises continuous irradiationduring propagation of an energy along a path to perform a transformation24. The apparatus of claim 16, wherein the one or more controllers isprogrammed to (i) direct the first energy beam, the second energy beamand/or the third energy beam to propagate via tiling propagation scheme.25. The apparatus of claim 24, wherein tiling comprises (1) irradiatinga first position along a path with a stationary or substantiallystationary energy beam to perform a first transformation directlyfollowed by (2) propagation along a path without transformation,directly followed by (3) repeating (1) and (2) until reaching an end ofthe path.
 26. The apparatus of claim 15, wherein the one or morecontrollers is programmed to direct forming a plurality of layers of theporous matrix during (b).
 27. The apparatus of claim 15, wherein (b)comprises directing the energy beam to transform the secondpre-transformed material to the second transformed material, wherein theone or more controllers that is programed to direct adjusting one ormore characteristics of the energy beam before and/or during (c). 28.The apparatus of claim 15, wherein the one or more controllers isprogrammed to direct (b) such that the second transformed material has ahorizontally non-overlapping portion with respect to the firsttransformed material.